Grim reapers have recently been employed in an argument against an infinite past (see here and here). I’d like to see if grim reapers may similarly be employed in an argument against uncaused beginnings.
I will begin with a preliminary comment about the modal reasoning involved in a grim reaper argument. Then I’ll review the grim reaper argument against an infinite past. Then I’ll present a new, parallel grim reaper argument against uncaused beginnings.
As I see it, the grim reaper argument against an infinite past is an instance of modal reasoning in which one attempts to subtract credence from a modal claim by “connecting it” with a modal claim that’s evidently false. To illustrate, consider the following argument against the possibility of time travel:
(1) Suppose I could go back in time.
(2) Then I could go back to a time before I was born.
(3) If I could go back to a time before I was born, I could prevent my birth.
(4) If I could prevent my birth, then I could exist without having been born.
(5) I cannot exist without having been born.
(6) Therefore, I cannot go back in time.
In the above example, we start with a somewhat “unclear” (and controversial) modal claim about time travel and then attempt to connect it via a series of (arguably) plausible premises to a claim that is easier to assess. This argument is just an example. Even if this particular argument isn’t sound, you get the gist of the strategy.
The gist (or outline) of a grim reaper argument against an infinite past is something like this.

Suppose an infinite past (infinite sequence of past events) is possible. Then it would seem to be possible for there to have been any combination of events throughout an infinite past. Thus, it would seem to be possible for there to have always been (say) a factory that each year produces a grim reaper (GR), which is a device set to produce a certain event–such as killing a poor guy named Fred–at a set time if and only if the grim reaper detects that this event hasn’t already been produced. Moreover, any combination of sizes, locations, check-rates, and “attack” times would seem to be possible (to avoid arbitrary modal cut-offs). Therefore, it would seem to be possible to setup a Grim Reaper scenario, which is a scenario in which the most recently produced GR is set to kill Fred at 12:30pm on date X, and each preceding GR is set to kill Fred at time 12:30pm – n / 2 on date X, where n is the number of years ago the GR was created. A GR scenario would seem to be impossible, however, because in it Fred dies at the hand of a GR by 12:30pm (since each is set to kill Fred before then–without prevention), yet no GR kills Fred (since a previous one would already have done so).
I’ll call this style of argument ‘Grim Reapers against an Infinite Past’–or ‘GRAIP’, for short.
I will leave open whether or not GRAIP is sound. Speaking for myself, I was agnostic about the possibility of an infinite past when I first encountered GRAIP, and GRAIP tipped me over into doubting that an infinite past is possible. So, the argument seems to have some merit (at least in my own thinking). That said, the argument is certainly not knockdown: one might resist one of the premises if one feels more confident that an infinite past is actually possible. But let us leave open for the sake of argument whether or not GRAIP is sound or in any way meritorious.
I’d like to consider whether GRAIP generalizes to produce other arguments for interesting conclusions. In particular, I am interested in the following conditional: if GRAIP is a good argument, then so is a grim reaper argument against uncaused beginnings–GRAUB.
Here is a gist (or outline) of GRAUB. Suppose uncaused beginnings are possible. Then it would seem to be possible for there to have been any combination of events (beginnings) that occur without a cause. Why should size or shape or degree of causal capacity of things that begin to exist make a modal difference here? It seems they wouldn’t. Thus, it would seem to be possible for any number and any combination of GRs to come into existence uncaused. But then it follows that it would be possible for a grim reaper scenario to obtain without a cause. Thus, since a grim reaper scenario is impossible, so are uncaused beginnings.
This argument seems to me to be parallel to the original grim reaper argument. I propose, then, that if GRAIP is sound or meritorious, so is GRAUB. (And of course, if GRAUB is not sound or meritorious, then neither is GRAIP.)
I turn, finally, to another GR argument, which if parallel, may cause concern for some defenders of GRAIP. This argument (brought to my attention by a friend of mine) is basically this. Suppose God is omnipotent and so can produce at any moment any possible GR. Then God could produce at once any combination of GRs, including that combination which results in the paradoxical GR scenario. Therefore, an omnipotent God doesn’t exist. Or: GRAIP is a bad argument (my friend’s conclusion). Call this last argument ‘Grim Reapers against God’–GRAG.
I am not sure what to think about GRAG. Is it parallel to GRAUB or GRAIP? Here is a reason one might think not. Perhaps God (unlike “nothingness” or an infinite past) is necessarily constrained by a rational nature not to produce contradictory scenarios. Furthermore, it may be that if God exists, then there is no possible omnipotent being distinct from God. If so, then we could explain why the GR scenario can’t obtain in terms of the nature of the foundational element of every causal chain. Incidentally, this proposal seems to neatly fall out of Alex Pruss’s theory of modality, according to which what is possible is grounded in the causal capacities of things within the actual history of causes.
Another idea (proposed to me by Alex Pruss) is that God operates trans-temporally and so doesn’t make a fresh decision at every moment concerning what things to create. Uncaused beginnings, by contrast, don’t operate trans-temporally.
Another idea is that there is a problem with producing an actual infinite number of events. This third idea, if correct, would seem to block the grim reaper argument against uncaused beginnings. But it would reinforce the argument for a finite past.
Your thoughts are welcome.

I’d never heard “Grim reapers”, I remember this as a supertask paradox which Wikipedia helpfully tells me is due to Benardete (1964).
Oddly, I recall uncaused events at limit times as a resolution to GRAIP. Suppose GR number N is set to kill Fred at time 1/N if he is not already dead. Then Fred simply dies at time 0 without cause — or at least, without any particular GR being the cause. (This is still an argument against computational supertasks, because it means you can’t rely on your memory bits to behave causally at limit times.)

In defense of GRAIP: even if an uncaused event is possible, why should a particular arrangement of GRs necessitate an uncaused event? Plus, if uncaused events are possible, then you still get a grim reaper scenario by GRAUB!

Hi, Joshua,
An alternative to GRAG that might avoid the issue of the properties of God would be an argument against infinitely many angels (say, GRAIA) in which God does not give them any specific command.
Let’s assume that GRAIP succeeds, that infinitely many angels in a finite past are possible, and that {Angel#n}, for all natural n, exist in 2013.
Let’s say for each n, that some day in 2013, Angel#n makes the following decision:
On January 1st, 2014, for some fixed t0, at some time between (t0 + 1/n+1 and t0+1/n), I will assert ‘ I’m [name of Angel#n]’.
Then, if the angels do as they chose, there will be an infinite series of events, one after the other, contradicting the assumption that GRAIP succeeds. The reasoning in GRAIA seems similar to GRAIP to me.
A potential objection would be that time is not possibly dense, but if that objection worked against GRAIA, I don’t see why it wouldn’t work against GRAIP.
I guess another potential objection would be that each angel might have a necessary speed limit, but I don’t see why there couldn’t be for each n an angel fast enough to assert (including saying it to herself) ‘ I’m ‘ in less than 1/(n*(n+1)) seconds); plus if that objection succeeded, that too would seem to similarly block GRAIP.
So, based on that, I would suggest that if GRAIP succeeds, then GRAIA succeeds. But if GRAIA succeeds, then apparently there is a problem with infinite angels, and plausibly so with infinitely many GR (if not with all actual infinities, but that’s not required), which as you point out would seem to block GRAUB.
Yes, granted, someone might say that God would not allow the angels to make those assertions. But that reply works against the reapers too, it seems to me.

Maybe the best explanation of why the GRAIP scenario is impossible is not that there is no possibility of an infinite past, but that it is not possible for a single thing (object, event, etc.) to have infinitely many things in its causal history. But where you have infinitely many angels who can potentially kill Fred (directly or indirectly), Fred’s life depends causally on infinitely many things.
If that’s right, then there could not be infinitely many angels that have causal influence over the same place in spacetime. But perhaps God could make infinitely many causally isolated universes (apart from the interconnection provided by their common cause) with a finite number of angels in each.

In discussion in our lounge, I gave a structurally similar argument against instantaneous causation. We talked about the Grandfather Paradox and backwards causation. And one person made the interesting remark that there has to be something wrong with my argument because it (or, rather, arguments of this sort) proves too much. We didn’t talk about GRs, but the remark can be extended to GRAIP. Arguments of this sort prove too much. They show that backwards causation is impossible, that instantaneous causation is impossible, that there can’t be an infinite past and that there can’t be an actual infinity of angels. That’s just too much to hang on such an argument form.
I am not sure how convinced I am by the “too much” move.
Here’s a deep common assumption in all of these arguments: They all assume a causal powers view of causation, rather than a Humean one. You can’t run these arguments on Humean views of causation, as on Humean views of causation what causes what depends on how stuff is arranged. These arguments all require rearranging stuff in the universe while keeping the causal powers unchanged. The Humeans allow rearrangement of stuff in the universe, but insist that the causal powers will change depending on what goes where.
I wonder if what all of these arguments might not be doing is showing that the distinction between the Humean and the causal powerist is rather more far-reaching than one might think. Maybe the causal powerist has to believe in the PSR, cannot accept an infinite past or other actual infinites, and must deny the possibility of instantaneous or backwards causation, while the Humean will accept all of these.
If so, that would show that there is actually quite a lot at stake in debates about causal powers.

Joshua,
While I don’t find the approach that someone or something would have to prevent a contradiction in these arguments persuasive, assuming that God’s being rationally required to prevent a contradiction would block GRAG (so, he can still make infinitely many angels), then it seems to me that it also blocks GRAIP, and for the same reason, assuming God exists.
Regarding GRAUB, I’m not sure it’s required if God exists; could God set up some place in which (say) finitely many things can come into existence uncaused, or would God count as a cause in such a case?
Anyway, one may wonder: what if we don’t make the assumption that God exists?
As before, going by the idea that something would have to prevent a contradiction, I suppose that line of argument would lead to a necessary concrete object with powers and dispositions that block a contradiction, even if it might be (say) a multiverse with some powers and dispositions (which we could call perhaps ‘laws of nature’) that are consistent, so no contradiction will happen, even if there are infinitely many galaxies and/or parallel universes and/or years.
Regarding GRAUB, a question here is whether something that comes into existence in a non-deterministic universe very rarely (and so, the probability would be low in a specific case, if a rational agent were to make an assessment of the probability of some O coming into existence, given the past), would count as uncaused or caused because they were previous conditions that made it improbable but allowed it.
If it’s the former, it seems to me that uncaused beginnings aren’t blocked.
If it’s the latter, they are blocked, but if it’s the latter, it’s hard for me to see how the usual examples of hypothetical uncaused bricks, horses, etc., should be called ‘uncaused’,

Alexander Pruss,
Regarding the common assumptions in these arguments, I think there might also be an implicit commitment to rejecting compatibilism.
For instance, is premise (2) of the grandfather argument above, true?
Is (2) true?
If one understands ‘could’ in the sense of possibility, even if I could go back in time, it would only be possible to go back in time to a time at which one’s future self already came through a time portal (or machine, etc.) – else, there is a contradiction right away, without having to do anything to one’s grandfather -, and of course, in none of those cases one killed one’s grandfather (or let’s say one’s younger self, to circumvent issues like when the grandfather is killed, whether artificial insemination was used, etc.). On the other hand, given a certain past, it would be impossible not to jump back in time to a time at which in the past, one’s future self already came through a time portal.
Understanding ‘could’ on a compatibilist sense of power, however, it’s not clear to me that one couldn’t go back in time and kill one’s younger self. For instance, let’s say that Bob ponders whether to go back in time and kill himself one day ago. Since he wasn’t killed by his future self, that’s not going to happen. Does that mean that, in a compatibilist sense, he cannot do it?
For that matter, if determinism is true, then given a certain past, it would be impossible to do anything but whatever is determined by that given past, even though one could do otherwise in the sense of ‘could’ that means ‘having the power to’, in a compatibilist sense of power.
Perhaps, a relevant difference between time travel and powers to change the future even on determinism is that on compatibilism, it’s impossible to do other than some X given a certain past, but on the other hand, arguably killing one’s younger self is arguably impossible even if the past is different, yet:
a. I’m not convinced that that difference would capture the proper view of power on compatibilism.
b. In any case, there are consistent scenarios with different pasts in which Bob kills his younger self, who later comes back to life.

Joshua,
I agree that if the Grim Reaper scenario is impossible, then an uncaused infinity of grim reaper’s will be impossible as well. But, the impossibility of an infinite sequence of uncaused grim reapers will be grounded in the impossibility of an infinite sequence of reapers right? Hence, the notion of being “uncaused” is not adding a layer of impossibility. Notice, one can’t argue that caused events are impossible because an infinite series of caused grim reapers is impossible.

Joshua,
While I don’t find the approach that someone or something would have to prevent a contradiction in these arguments persuasive, assuming that God’s being rationally required to prevent a contradiction would block GRAG (so, he can still make infinitely many angels), then it seems to me that it also blocks GRAIP, and for the same reason, assuming God exists.
Regarding GRAUB, I’m not sure it’s required if God exists; could God set up some place in which (say) finitely many things can come into existence uncaused, or would God count as a cause in such a case?
Anyway, one may wonder: what if we don’t make the assumption that God exists?
As before, going by the idea that something would have to prevent a contradiction, I suppose that line of argument would lead to a necessary concrete object with powers and dispositions that block a contradiction, even if it might be (say) a multiverse with some powers and dispositions (which we could call perhaps ‘laws of nature’) that are consistent, so no contradiction will happen, even if there are infinitely many galaxies and/or parallel universes and/or years.
Regarding GRAUB, a question here is whether something that comes into existence in a non-deterministic universe very rarely (and so, the probability would be low in a specific case, if a rational agent were to make an assessment of the probability of some O coming into existence, given the past), would count as uncaused or caused because they were previous conditions that made it improbable but allowed it.
If it’s the former, it seems to me that uncaused beginnings aren’t blocked.
If it’s the latter, they are blocked, but if it’s the latter, it’s hard for me to see how the usual examples of hypothetical uncaused bricks, horses, etc., should be called ‘uncaused’,

It seems to come down to this question: what prevents individually possible GRs from being combined into a GR scenario?
If the basic explanation is that there is a problem with infinitely many events, then it seems GRAIP is good, but GRAUB is not. (Re: Aaron)
If the basic explanation is that nothing can be causally preceded by infinitely many things, then it seems GRAIP and GRAUB could both be good (in principle). (Re: Alex)
If the basic explanation is that God (or some other necessary foundation) is rationally required to prevent absurdities, then it seems to me GRAUB is good (assuming God can’t “setup” uncaused events), but GRAIP is not. (Re: Angra.)
I am now wondering if the basic explanation could be psr, since this explanation would seem to unite the cases. So, for example, an infinite past per se is okay, as long as there is an ultimate explanation of that past–perhaps in terms of a rational, necessary foundation. But without an ultimate explanation of the infinite past, any arbitrary (unexplained) combination of infinite events would seem to be possible–giving us the possibility of a GR scenario.
Similarly, if uncaused events are possible, then any combination of *individually* possible uncaused GRs would seem to be possible–giving us the possibility of a GR scenario.
The infinite angels and infinite universes may be okay. But given psr, absurd combinations are not possible, since every combination is ultimately explained, perhaps by a rational foundation or something else.
If so, then the lesson is this: without psr (or some such general principle of explanation), “anything” can happen, including the paradoxical GR scenario.

Joshua,
My take on this is that that’s not the question. What prevents them from being combined would be, in my view, a question if we were talking about the actual world, or worlds with the same initial segment. But in that case, an answer would be that there simply aren’t so many reapers, and the causal structure of all of causal reality is such that no such reapers can come into existence.
On the other hand, if we’re talking about metaphysical possibility, I don’t think that anything has to prevent them from doing that, since there are no reapers or realm in which they might come into existence ‘out there’ so to speak; rather, some scenarios are contradictory (and thus impossible), and others (with an infinite past, infinitely many reapers, etc.) are not contradictory, even after considering the meaning of words, including rigid designators.
But leaving that aside and assuming that this type of GR like of argument is successful, in that context, some of my impressions at this point are:
a. I’m not sure why some event couldn’t be causally preceded by infinitely many ones, as long as infinitely many angels in causally isolated universes are possible, since that would be an example of infinitely many things in which they do not have the power to bring about a contradiction, but it seems similar to me that an infinite series of past events in which nothing has the power to bring about a contradiction.
b. Regarding the PSR, I’m not sure it’s required. For instance, there might be no explanation as to why, say, a particle decays before T0 (why not after?), but even then, the kind of things that can happen is within a certain range, constrained by the causal structure of the world resulting from some necessary cause. If so, some things could happen without an explanation, but not everything.

Angra,
Thanks. Yeah I was using “prevents” loosely. I mean something like this: what accounts for why there cannot be any arbitrary combination of individually possible GRs?
There are many potential explanations. I am wondering if psr may provide the deepest and simplest.
But no infinite (past) events is a good contender.
(I think I’m sympathetic with your (a), less so with (b) for simplicity considerations…)

Joshua,
Thanks for the clarification, and sorry if I misunderstood.
On the question you ask, my view would be that what accounts for why there cannot be any arbitrary combination of individually possible GR (if it needs accounting for), or more precisely, why not any arbitrary scenario involving an arbitrary combination of individually possible GR is possible, is the fact that some such scenarios are contradictory, and contradictions cannot obtain.
In other words, I don’t get the impression that one would need another explanation (i.e., beyond its being contradictory) as to why it’s impossible.
As I see it, the matter would be different in a case of causal possibility in the actual world or one that can branch from the actual world, because we could still ask why causally some event won’t happen (we know that it won’t because that would be a contradiction, but what causally prevents it from happening), but I don’t see why that would apply to a contradictory scenario.

Joshua,
Regarding (b), I would say that simplicity favors determinism over any usual kind of indeterminism, but if one does not rule out indeterminism in all usual forms (and I don’t think one should rule it out on simplicity considerations), then I’m not sure how (b) could be ruled out.
For instance, rejecting (b) would seem to rule out indeterminism in Quantum Mechanics (e.g., on an indeterministic interpretation, there would be no explanation as to why the particle decays before t0, rather than at or after t0).
But also, it seems to me that rejecting (b). would imply that no form of indeterminism is true.
Granted, someone might hold that indeterministic libertarian freedom wouldn’t have a problem; I don’t see indeterministic libertarian freedom as a form of freedom, but in any case, if it could happen that, given the state of the world at some time t (including all of the reasons an agent has for taking certain actions), both X or Â¬X are possible (and, let’s say neither one of them is more probable than the other one, if there is some non-epistemic and not frequentist probability), then there would seem to be no explanation as to why X, rather than Â¬X; that a certain agent had reasons R for A would seem to be a reason, since for that matter the agent had those very same reasons (and everything else was the same), so there would be no explanation as to why X, rather than Â¬X.
Also granted, libertarians usually don’t agree with that, and often take the reasons R based on which agent A brings about X to be the explanation of X, even if A also had reasons T for Â¬X, and even if given the state of the world before A’s decision, either choice was still possible, and neither one of them was more probable than the other. Personally, though, I don’t find R to be an explanation as to why X happened, rather than Â¬X, given that it was also possible and no less probable given the previous state (including R) that Â¬X would be the case.
In any case, even assuming that libertarians are correct about that (i.e., about there being an explanation in R in a case such as the previous one), then still rejecting (b) would seem to be a rejection of any form of indeterminism not involving the actions of agents. As I see it, indeterminism in cases involving agents but determinism about everything else is weak on the simplicity front, especially given the kind of discontinuity in living organisms that it would seem to imply.

As I see it, the matter would be different in a case of causal possibility in the actual world
Interestingly, on Pruss’ theory of modality, metaphysical possibility collapses to causal possibility in the actual world.

That’s an interesting theory, which would have some advantages and some disadvantages in my view, though personally I’m not convinced (my take on modality is close to Swinburne’s).
The assumption that Pruss’ theory is correct, though, would limit what I would be inclined to accept as metaphysically possible, to a considerable extent (actually, I would find it plausible that if metaphysical possibility collapses to causal possibility in the actual world, it may well collapse to nomological possibility as well).
For instance, I would not be inclined to accept any principles based on imagination (beyond what’s based on what we already know, or what we can predict as probable based on that), conceivability, or continuity, since I’m not sure why any of them would be a good guide to knowing the causal structure of the actual world.
Similarly, I would not be inclined to accept angels, ghosts, grim reapers, sending information faster than light, etc., as metaphysically possible.
On the other hand, I would find a metaphysically necessary concrete object (e.g., the universe, in some sense of ‘universe’) to be considerably more plausible than I do now, though that wouldn’t rule out infinite causal regress between states of that object.

This is from Angra to Alexander Pruss:
Hi,
Regarding the common assumptions in these arguments, I think that in addition to other assumptions, there might be an implicit commitment to rejecting compatibilism, at least in the grandfather argument or similar ones.
For instance, is premise (2) of the grandfather argument above, true?
If one understands ‘could’ in the sense of possibility, even if I could go back in time, it would only be possible to go back in time to a time at which one’s future self already came through a time portal (or machine, etc.) – else, there is a contradiction right away, without having to do anything to one’s grandfather -, and of course, in none of those cases one killed one’s grandfather (or let’s say one’s younger self, to circumvent issues like when the grandfather is killed, whether artificial insemination was used, etc.). On the other hand, given a certain past, it would be impossible not to jump back in time to a time at which in the past, one’s future self already came through a time portal.
Understanding ‘could’ on a compatibilist sense of power, however, it’s not clear to me that one couldn’t go back in time and kill one’s younger self. For instance, let’s say that Bob ponders whether to go back in time and kill himself one day ago. Since he wasn’t killed by his future self, that’s not going to happen.
Does that mean that, in a compatibilist sense, he cannot do it, even if time travel is possible, or that a contradiction is entailed if he can?
I doesn’t look like that to me.
For instance, if determinism is true, then given a certain past, it would be impossible to do anything but whatever is determined by that given past, even though one could do otherwise in the sense of ‘could’ that means ‘having the power to’, in a compatibilist sense of power.
But that seems similar to the time travel scenario to me, in terms of power to do stuff.
Perhaps, it might be argued that a relevant difference between time travel and powers to change the future even on determinism is that on compatibilism, it’s impossible to do other than some X given a certain past, but on the other hand, arguably killing one’s younger self is arguably impossible even if the past is different, yet:
a. I’m not convinced that that difference would capture the proper view of power on compatibilism.
b. In any case, there are consistent scenarios with different pasts in which Bob kills his younger self, who later comes back to life.
So, it seems to me that the grandfather argument plausibly doesn’t work under compatibilism.
If it is, that would mean that one does not have the power to kill one’s younger self, but that would not seem to block time travel to the past and to regions of space that are past-future causally disconnected from one’s future (perhaps, akin to the case of infinite universes with infinitely many angels in it).
the explanation that GRAIP is impossible because there cannot be a single thing that causally depends on infinitely many ones, that would seem to raise issues about what counts as a “thing”.
For instance, if one goes by a usual definition of ‘universe’ in the KCA, like ‘the whole of material reality’ (leaving aside issues of vagueness of ‘material’), it seems to me that if there were infinitely many galaxies, the universe at the a given time would causally depend on infinitely many past states of it. Would that meant that there cannot be infinitely many galaxies?

Some quick thoughts:
1. If there were infinitely many galaxies but the past was finite, only finitely many of the galaxies would be in the backwards light cone of any bounded event, and hence in the causal past of that event.
2. I don’t think compatibilism is needed. Imagine a machine that has the power to annihilate its maker before the maker made it. And suppose the machine’s functioning is indeterministic.
3. I don’t see why it is any more mysterious that our modal intuitions would give us insight into the causal structure of this world than that our intuitions would give us insight into whatever it is that grounds mathematical or ethical truths (and, of course, it won’t help if these truths aren’t grounded). Of course, unless theism is true, it is surprising that our intuitions give us insight into that which grounds mathematics or ethics.

Angra:
“Personally, though, I don’t find R to be an explanation as to why X happened, rather than Â¬X, given that it was also possible and no less probable given the previous state (including R) that Â¬X would be the case.”
But notice that quite possibly P(X|R) is large. Granted if S are the reasons for ~X, then P(X|S and R) may be 1/2 or smaller. But it’s not (S and R) that is being proposed as an explanation for X, but R.

Joshua,
GRAIP doesn’t work because the contradiction in the scenario can be resolved just as easily by denying that Fred must be alive at some point as it can by denying an infinite past. Hence, there is no compelling reason to think that an infinite past must be the problem in this case. Without getting into specifics, Koons’s argument runs into the same problem.

Hello,
Infinity is a favorite topic of mine, so this seems like a good post for my first comment.
There is good reason to think that the impossibility of the various Grim Reaper scenarios is due to the fact that they are contradictory and need not be explained by further principles about infinity or causal dependence. We can strip away all relation to time, space or causation and get the same result in pure mathematics. Unless there is a problem with infinities in mathematics, infinities cannot be the problem in the other scenarios.
To show this, define a “reap pair” as a pair of functions such that:
1. f and g are functions from (0,1) into {0, 1}.
2. g(x) = 1 iff g(y) = 0 for all y less than x.
3. g(x) = 0 only if f(x) = 0.
4. f(x) = 0 only if there exists a y less than x such that g(y) = 1.
(All quantifiers restricted to (0, 1).)
We can prove that there is no reap pair. First, proof that g(x) = 0 for all x. Assume for reductio that g(x)= 1 for some x. By 2 every g(y) for y less than x must be 0. Thus, also by 2, every g(y) for y less than x must be 1, since there is no lowest member of the domain. Contradiction, so g(x) = 0 for all x.
By 3, it then follows that f(x)= 0 for all x.
Then by 4 it follows that there is some y such that g(y) = 1. But we proved there was no such y. Contradiction. Thus, there can be no reap pair.
The Grim Reaper scenarios all try to set up reap pairs: for the original GR scenario, map times between 8 and 9am to (0,1). Treat g(x) as a function that is 1 iff a grim reaper kills the person at instant x. Treat f(x) as a function that is 1 iff the subject is alive at time x. The infinite set of grim reapers defined as they are causes a problem because the dependence of their actions and the subject’s status must be a reap pair. But this is impossible, hence the paradox.
It appears then that infinity has nothing to do with it. If GR scenarios cause trouble for infinity in a physical world, do they therefore cause trouble for infinity in pure mathematics? Presumably not. The only sense in which infinity played a role in the proof that reap pairs do not exist is that the reals are dense, allowing there to be no smallest member of the domain. I take it the proof does not show the absurdity of the real numbers.
To me this is similar to the fact that one cannot square a circle or trisect an angle. It seems like it should be possible to do either: just perform finitely many of steps in construction until you have squared a circle. But it is impossible. So are grim reaper scenarios. But actual infinity may still be possible. The implications of reap pairs do not spread like a disease to other proposed arrangements of infinity many objects.

Certainly arguments of this sort are tricksy. But imagine this. Each GR has a dial on its back where its activation time, between noon and 1 pm, is set. GR #1 is set for noon. For n > 1, GR #n is set for noon + 1/n hours.
There is no contradiction, mathematical or otherwise. Fred dies at noon in this story.
But suppose someone instead came along and destroyed GR #1 before noon, leaving the others untouched. That would lead to a contradiction, as it would leave us with just the classic impossible scenario.
But isn’t it really weird that we should have a possible setup with an infinite number of entities with such-and-such causal powers, but if we imagine one of them disappearing, we get an impossible setup?

Benjamin,
2 is sufficient to rule out the existence of such a function g.
Alex,
I was just about to say that your GR scenario is better in that the possibility of Fred being alive at some point isn’t an issue. In your scenario the problem is either the infinitude of the past or the density of time, nevertheless that the conjunction of those two claims must be false is interesting.
“But isn’t it really weird that we should have a possible setup with an infinite number of entities with such-and-such causal powers, but if we imagine one of them disappearing, we get an impossible setup?”
But the original setup can’t be possible because then the modified setup would be possible (just eliminate GR #1).

Alexander Pruss,
(1) Right, that would be the case of bounded events if one accepts that time is relative, which I do (by the way, I think that that might raise some interesting side issues (e.g., let’s say that there are astronauts on Mars, and one of them prays to God so that he allows her to communicate with her husband with less than a five second delay; can God do it?)), but my suggestion, perhaps unclear*, was that the thing in question (e.g., that the object or things with infinitely many events in its past) was the whole universe, which seems to be counted as an object or thing in the context of the KCA and a number of other arguments.
*Side note: I excluded the part that begins with “the explanation that GRAIP ” from the post I sent in that reply to you (I copied and pasted the rest; the last part was something I had been thinking about but wasn’t ready to be posted), but then it seems the post was lost and I sent the whole file to Joshua, so my mistake.
(2) While I don’t know how to imagine such machine, there seems to be a misunderstanding.
What I was arguing for wasn’t that compatibilism was needed for the argument to work, but on the contrary, that the argument against time travel based on the grandfather scenario does not appear to work under compatibilism (i.e., I think rejecting compatibilism is needed; assuming indeterminism would suffice too, but if indeterminism is assumed, there is no need to include the grandfather to reach the contradiction, it seems to me).
(3) I wouldn’t be inclined to accept that intuitions about conceivability and/or imagination would be modal intuitions on the causal view.
Imagination and conceivability (in different forms) would still give us (in combination with searching for contradictions. etc.) insights about what is not contradictory, even after considering the meaning of the words (including rigid designators), precisely because we can find no contradictions in some scenarios we appear to be able to conceive, imagine, etc., but I don’t see why what we can imagine, in some sense conceive of, etc., would be connected to what can be causally achieved by entities that actually exist.
Granted, someone might assume theism (for instance) and then make a case for that connection, but I don’t make that assumption.
Regarding the ‘grounding’ of ethical or mathematical truths, I’m not sure what you mean by ‘grounding’ (perhaps, some examples of grounding of other truths might help), but generally, I don’t find it particularly surprising that we have the means to think about mathematics, or ethics, or do philosophy about them given our general category for abstract thinking.

The following is another GR argument that strikes me as similar to the ones against an infinite past, and which also seems to prove too much in my view (though that is not the main reason why I don’t find these kind of arguments persuasive), though for those who accept GR arguments, perhaps the following would be a simplification of an argument against temporal density.
Let’s say that agents capable of checking whether Fred is alive and killing him at any arbitrarily high finite speed are possible, and that time is possibly dense.
Then, the following scenario would be possible:
There are two grim reapers, Odd and Even. They both have the power to check whether Fred is alive as fast as they want, and also the power to kill him as fast as they want.
So, Odd has dispositions to act as follows:
1. For all n, check whether Fred is alive at some time t between (noon + (1/(2n+1))) and (noon+(1/(2n+2))), where the added numbers are numbers of seconds.
2. If he is dead, do nothing.
3. If he’s alive, kill him before the end of the interval.
On the other hand, Even has dispositions to act as follows:
1. For all n, check whether Fred is alive at some time t between (noon + (1/(2n))) and (noon+(1/(2n+1))), where the added numbers are numbers of seconds.
2. If he is dead, do nothing.
3. If he’s alive, kill him before the end of the interval.
Nothing else kills Fred.
Then, a contradiction follows. We can even derive a contradiction using a single reaper, who checks whether Fred is dead or alive, in some increasingly short non-overlapping intervals and then acts or not depending on that.
Granted, a potential objection would be beings that are arbitrarily fast aren’t possible, though that would seem to be problematic for theism.

Alexander,
“But notice that quite possibly P(X|R) is large. Granted if S are the reasons for ~X, then P(X|S and R) may be 1/2 or smaller. But it’s not (S and R) that is being proposed as an explanation for X, but R. ”
In my assessment, that would not work as an explanation, as it would ignore relevant information that we actually have.
For instance, let’s consider the following scenario:
Fact R: Jones is a bicycle enthusiast who, for years up till 2013, he’s not used another means of transportation in the city (other than walking), and he really likes going to work on his bicycle.
Fact S: On January 1st 2013, Jones had an accident, and his spine was broken.
The fact to be explained (X) is that Jones went to work (a 20 miles trip) on January 2nd, on his bicycle.
It seems to me that P(X|R) is large, but that wouldn’t mean that R is an explanation for X.
More precisely, R plausibly should be accepted as an explanation for X by someone who does not know S, but if someone knows S, clearly R does not explain X to that person, no matter how large P(X|R) is.
The point I’m trying to make is that what explains a fact to a given person depends on what the person knows, and in this case, what might be a good explanation before considering certain information is no longer a good explanation after that.
Granted, there are some complicated issues here, to be sure, such as:
a. In these cases explanations are relative to agents.
b. The type of probability involved here seems to be (usually, if not always) epistemic probability.
Even so, in my assessment those issues do not seem to favor the type of explanation offered in the case of libertarian free will, since.
a. In the context of the PSR, ‘there is an explanation’ seems to be about ideal conditions, at least for human agents, or maybe even all rational agents. The condition that there is an explanation of a fact F would not appear to be satisfied by the fact there is some human agent H and some facts L such that H should accept L as an explanation for F given H’s epistemic position, but H ought to reject L as an explanation if she had better information.
Side note: Personally, I think that many arguments involving explanatory principles would be more clear if they gave more information on the type of agent (including epistemic position) the explanation is meant to persuade.
b. I’m not sure there is another kind of probability, but assuming there is, the conclusion would be the same. If it’s in terms of propensity for something to happen, then it’s not a good explanation one that cites conditions that would make a fact probable, while leaving aside other facts that reduce such probability.
For instance, let’s say that some quantum event Q1 happened (assuming indeterminism in this particular example, plus some sort of non-epistemic probability, maybe in terms of propensities), and that made Q2. But then after Q1 before Q2 happened, Q3 happened, and Q3 made the probability of Q2 less than 1 in a trillion times a trillion.
Then, Q2 happened anyway, even though the probability that it would happen, given any previous states of the world arbitrarily close to the time at which Q2 happened, was less than 1 in a trillion times a trillion.
While Q1 might perhaps be cited as a remote indeterministic cause of Q2, it does not explain Q2, as far as I can tell (and I don’t think that saying that the world is just such that probably, some event in a category C happens, even if each individual event in C is extremely unlikely, would adequately explain why an individual event in C happens; the individual event in question would strike me as an unexplained event).
Perhaps, it might be argued that some other issue makes the explanation good in the case of the libertarian agent, but I don’t see why that would be so. In any case, the fact that maybe P(X|R) is large does not seem to support, in my view, the conclusion that R is a good explanation for X, as long as the probability of X given the other reasons, etc., was no greater than 1/2, and in some cases lower.

I do think that (on the most plausible rendering of the story) R explains X in the bicycle case. It just doesn’t explain as well as an explanation that also says how he managed to cycle despite a broken spine would.
But, certainly, high conditional probability is not sufficient (and I say: not necessary) for explanation.
My preferred method for explanation of quantum phenomena goes as follows. We want to explain why an electron in the normalized state 0.1000 |up> + 0.9801 |down< collapsed to |up> upon observation. That is explained by the following proposition:
(1) The electron’s wavefuntion was collapsed on the orthonormal basis |up> and |down>, and the wavefunction had a normalized modulus-square of the coefficient for |up> of at least 0.01 and a normalized modulus-square of the coefficient for |down> of at most 0.99.
If the state were to collapse to |down>, the explanation would instead be:
(2) The electron’s wavefuntion was collapsed on the orthonormal basis |up> and |down>, and the wavefunction had a normalized modulus-square of the coefficient for |up> of at most 0.01 and a normalized modulus-square of the coefficient for |down> of at least 0.99.
Note that the two explanations are different, which gives at least a little bit of contrastivity. But even if there isn’t contrastivity, the PSR doesn’t say that for every truth p and relevant alternative q there is an explanation why p rather than q holds. The PSR says that for every truth p there is an explanation why p holds.

On the issue of the bicycle, I would say that R might be offered as part of an explanation. However, if there is no better explanation than R (plus, at most, other facts about Jones’ motivation, and generally about his state of mind), it seems to me that X is not explained (i.e., the PSR would not be true in that case).
Similarly, on indeterministic QM, I don’t think that (1) explains it; also, we may consider phenomena in which no observations appear to occur (e.g., radioactive decay), but also I don’t find the account as to why it happened persuasive (i.e., I don’t intuitively find that it explains why it happened.
I guess we may have to leave that point at that, due to different intuitions.
Side note: Just to clarify my take on this, I’m a compatibilist and take no stance on whether determinism is true (though I would say it is true assuming God exists and knows the future beyond probabilistic assessments; but that’s another issue), so my assessment that in cases like the ones described above there would be no explanation don’t lead me to conclude that the PSR is false.

True, in some cases of radioactive decay, there is an observation. In the vast majority of cases, there isn’t.
Sorry if I wasn’t clear enough; I was thinking of all of the other cases of radioactive decay, before there were any Geiger counters, or any animals for that matter (granted, someone might suggest that God makes observations).
Of course, all other quantum phenomena also happen without observations, but I thought I’d mention radioactive decay because there wasn’t much room for objections (God’s intervention aside), since we use different types of radiometric dating to date the ages of fossils, rocks, etc., some of which are based on some types of radioactive decay that happened before there were any humans, before any animals, and in some cases, even where there was no life.

“Of course, all other quantum phenomena also happen without observations”
Let me preface this by saying I don’t work in philosophy of quantum mechanics. It seems that on the traditional interpretation, we have deterministic evolution via the Schrodinger equation until something is observed, at which point collapse happens. It need not, however, be an observation precisely of the observable in question, because in practice there is ever-spreading entanglement between the observable in question and other stuff, so that in practice pretty quickly something entangled with the observable in question is apt to get observed.

I’m no expert in QM or its philosophy, either, by the way.
Anyway, I’d like to ask a couple of questions for clarification purposes, in order to address your points:
1. When you say “the traditional interpretation”, are you talking about the Copenhagen interpretation or some version of it? (if it’s one of its versions, I’d like to ask which one).
2. When you mention ‘observers’, are you using ‘observer’ in a usual sense? More precisely, does the observer have to have some kind of subjective experience?

Yes, the Copenhagen interpretation. And, yes, I am using “observer” in the usual sense.
But I think this has gotten off-track. Even if there are continuous-time random processes (I suppose on Collapse interpretations, there are), we can still give a similar kind of story: Why did the decay happen between t1-epsilon and t1+epsilon? Because it had at least such-and-such (very small!) probability of happening there and at most such-and-such probability of happening elsewhere. It may not be a very good explanation, but the PSR doesn’t say anything about the quality of the explanation.

Iâd like to call your attention to a relatively recent interpretation of QM called the âmany mindsâ interpretation. It takes what QM says at face value, namely that physical reality consists of the deterministic evolution of a wave-like superposition of different physical states, each with a particular amplitude. According to the many minds interpretation this *is* physical reality. Now some of these states happen to include a physical structure (say a human brain) which produces conscious experience, and which, naturally enough, is of the physical values present in that particular state of reality, out of the many superposed ones.
If one is a scientific realist I think this is the interpretation one should embrace. Itâs the minimal one since it adds nothing to the theory itself (no conscious observations causing collapses, no splitting of the universe, no guiding waves), and beautifully solves the observation problem. When we look around we only see a concrete reality because thatâs the physical state of the universe that produces our experiences.[1]
In the case of sitting in a room and hearing a click from the Geiger counter, the many minds interpretation says that there is also a mind in the room which didnât hear that click, and also a mind that remembers hearing that click in the past. Or, actually, there is a potentially infinite number of minds with a distribution (of now hearing the click, not hearing the click, remembering having heard the click) defined by the amplitudes of QMâs wavefunction.
[1] The many minds interpretation does suffer from many of the absurdities of the many worlds interpretation (see, for example, quantum immortality), but it seems there is no way to be a physical realist about QM without assuming that the world is absurd. Me, being a Berkeleyan idealist, stand by and marvel at the spectacle of physical realists tying themselves up in knots.

Alexander,
Okay, thanks for the clarification.
Briefly, I see a few problems with the account you described above (i.e., based on entanglement), like:
1. The Copenhagen Interpretation has different versions (or if you like, different interpretations go by that name; e.g., see the SEP article on it), and wave function collapse may be interpreted as an epistemic matter, or as a phenomena about the system being described.
It seems that Bohr interpreted in the former way (e.g., see the SEP entry on “/qm-copenhagen/”), so even if he used ‘observer’ in the usual way, there was no causation in terms of wavefunction collapse (though he didn’t actually used the expression ‘collapse of the wave function’).
On the other hand, Heisenberg (while not using the term, either), seemed to consider the matter of collapse one of ontology, not an epistemic one. However, Heisenberg was not using ‘observer’ in the usual sense, and also was treating observers as classical systems (e.g., see Heisenberg’s quotation in the Wikipedia article on the Copenhagen Interpretation), which also is a problem (e.g., see Weinberg’s criticism in the same Wikipedia page).
2. If one uses ‘observer’ in the usual sense of the word and also considers the collapse of the wave function in a non-epistemic but ontological matter (perhaps, someone might use ‘realistic’ or ‘objective’ in this context, as opposed to ‘subjective’; I personally prefer not to, for a number of reasons, but I can use those terms if you like) – as in your suggestion, if I understand it correctly â would lead to a number of difficulties.
For example, we may consider again radioactive decay or some other event requiring measurements in the early Earth, before there was life, or even earlier, during the formation of the Solar System before there were any planets. Then no observer on Earth, or for that matter in our Solar System, measured them. The view that something entangled with them was measured would require that for every case of radioactive decay in the early Earth (or some of the other events), some alien organism from another planet made a measurement several light years or farther away, instantly causing radioactive decay of particles on Earth (unless a superpowerful entity like God is said to carry out the measurements, or something like that). Without a lot of evidence, I would not be inclined to accept something like that.
3. Moreover, one can push the matter further back in time, to a time before there were any planets in the universe (at least unless there is an infinite past, and even then, I don’t know that the proposed entanglement would work) and in that case, that eliminates all observers in the universe, committing the theory to some view from outside the universe or something like that (which might not be a difficulty for some theistic views, but that requires ontological commitments I’m not inclined to accept, apart from the fact that that’s not a mainstream view of QM).
Regarding the proposed probabilistic explanation of why the decay happened between t1-epsilon and t1+epsilon, I intuitively don’t find it to explain the phenomenon in question. Your point about the quality of the explanation seems interesting to me, but intuitively, I would be inclined to say that if one can tell an explanation isn’t a good one, one ought not to accept it. I guess there may be some issues about the meaning of ‘explanation’ and the kind of probability we’re talking about here.
By the way, and just to be sure, when you mention probability in this context, are you talking about some kind of propensity, rather than epistemic probability?
I’ve seen you mention ‘objective probability’ in other threads, but that term too has more than one interpretation.

In a many-minds kind of setting, the probability of some result R is going to have to be defined by the proportion of the number of minds (sharing a specified initial state) that observe R to the number of those that don’t. But given infinitely many minds, in typical cases, both numbers will be infinite. They will then either be infinities of the same cardinality, in which case no probability other than perhaps 1/2 can be defined, or they will be infinities of different cardinalities, in which case one of the probabilities will be infinitely close to 0 and the other will be infinitely close to 1. In particular, we will never get meaningful probabilities that aren’t close to 0, 1 or 1/2, and hence there will not be a way of making the account empirically adequate.
There might be some cases where you are one of infinitely many minds and there are well-defined probabilities. One kind of cases might be where you have genuinely stochastic processes leading to the states of mind, and you read the probabilities off the dispositions of the stochastic processes. But that won’t be the case for many-minds, since that would bring back the (allegedly) problematic indeterminism. The other kind of case is where there is a temporal or maybe spatial or similar ordering on the minds that lets you define frequencies via a non-arbitrary limiting process. But I don’t see where you’ll get a requisite ordering on the minds. And even if you did, I doubt that this option works, because self-locating probabilities should be permutation invariant.
“but it seems there is no way to be a physical realist about QM without assuming that the world is absurd”
I don’t see anything particularly absurd about the Copenhagen interpretation. Sure, it’s strange that minds should have the power to collapse wavefunctions, and on the von Neumann version the collapse is discontinuous (by the by, I am not sure it need be; I think we can imagine a continuous collapse process that ensures that conscious states are never superimposed), but neither consequence is absurd.

From Angra (he is having intermittent technically difficulties posting):
Alexander,
Thanks for the clarification.
Briefly, I see a few problems with the account you described above (i.e., based on entanglement), like:
1. The Copenhagen Interpretation has different versions (or if you like, different interpretations go by that name; e.g., see the SEP article on it), and wave function collapse may be interpreted as an epistemic matter, or as a phenomena about the system being described.
It seems that Bohr interpreted in the former way (e.g., see the SEP entry on “/qm-copenhagen/”), so even if he used ‘observer’ in the usual way, there was no causation in terms of wavefunction collapse (though he didn’t actually used the expression ‘collapse of the wave function’).
On the other hand, Heisenberg (while not using the term, either), seemed to consider the matter of collapse one of ontology, not an epistemic one. However, Heisenberg was not using ‘observer’ in the usual sense, and also was treating observers as classical systems (e.g., see Heisenberg’s quotation in the Wikipedia article on the Copenhagen Interpretation), which also is a problem (e.g., see Weinberg’s criticism in the same Wikipedia page).
2. If one uses ‘observer’ in the usual sense of the word and also considers the collapse of the wave function in a non-epistemic but ontological matter (perhaps, someone might use ‘realistic’ or ‘objective’ in this context, as opposed to ‘subjective’; I personally prefer not to, for a number of reasons, but I can use those terms if you like) – as in your suggestion, if I understand it correctly â would lead to a number of difficulties.
For example, we may consider again radioactive decay or some other event requiring measurements in the early Earth, before there was life, or even earlier, during the formation of the Solar System before there were any planets. Then no observer on Earth, or for that matter in our Solar System, measured them. The view that something entangled with them was measured would require that for every case of radioactive decay in the early Earth (or some of the other events), some alien organism from another planet made a measurement several light years or farther away, instantly causing radioactive decay of particles on Earth (unless a superpowerful entity like God is said to carry out the measurements, or something like that). Without a lot of evidence, I would not be inclined to accept something like that.
3. Moreover, one can push the matter further back in time, to a time before there were any planets in the universe (at least unless there is an infinite past, and even then, I don’t know that the proposed entanglement would work) and in that case, that eliminates all observers in the universe, committing the theory to some view from outside the universe or something like that (which might not be a difficulty for some theistic views, but that requires ontological commitments I’m not inclined to accept, apart from the fact that that’s not a mainstream view of QM).
Regarding the proposed probabilistic explanation of why the decay happened between t1-epsilon and t1+epsilon, I intuitively don’t find it to explain the phenomenon in question. Your point about the quality of the explanation seems interesting to me, but intuitively, I would be inclined to say that if one can tell an explanation isn’t a good one, one ought not to accept it. I guess there may be some issues about the meaning of ‘explanation’ and the kind of probability we’re talking about here.
By the way, and just to be sure, when you mention probability in this context, are you talking about some kind of propensity, rather than epistemic probability?
I’ve seen you mention ‘objective probability’ in other threads, but that term too has more than one interpretation.

1. An epistemic reading seems to be ruled out by Bell’s inequality.
2. Why not say that the universe was in a giant superposition state–including a superposition of states tied to different decay times–until the first conscious organisms evolve (this has been said)? Do we have any empirical reason to think that this wasn’t the case?
3. Yes, I’m talking about propensities.
Explanations seem to come in degrees. This is especially true of stochastic explanations. That the indeterministic die didn’t show 6 has a pretty good stochastic explanation. That it didn’t show 5 or 6 has a less good stochastic explanation. And so on down.
I accept Hume’s thesis that causes always explain effects. So where there is causation, even with a very low probability, we always have explanation. That Smith had syphilis explains that he got paresis, as the standard example in the literature goes, even though only a minority of syphilis sufferers get paresis. But where the probabilities are low, the explanation tends to be less good (or less strong–I don’t know which word I want to settle on).

1. Bell’s theorem doesn’t seem to be a problem for interpretations of QM that do not posit a wavefunction collapse (e.g., Many Worlds, Consistent Histories, Bohm), so I’m not sure why an epistemic interpretation would be ruled out by it. Do you have a source, or an argument to that conclusion?
2. I don’t know who made the suggestion or in which context (do you have a link and/or source?), but briefly, that would seem to entail (at least) rejecting our measurements of the age of rocks, the Earth, etc., as they require radioactive decay processes earlier than life on Earth, which would on that assumption require conscious lifeforms elsewhere in the universe causing the wave functions to collapse on Earth, and there seems to be no good evidence to assume that that was the case.
So, at least it seems to me that such an interpretation would be committed to rejecting much of modern geology of the distant past.
In addition to that, it seems to me that there are other processes that happened before the appearance of conscious lifeforms as far as we know.
3. a. Regarding the stochastic explanations you mention (e.g., the dice, syphilis), in normal cases those appear to be epistemic probabilities.
For instance, even if only a minority of those who suffer syphilis get paresis, there is no assumption as far as I can tell that given the state of the universe after he got paresis, it was still possible that he would not get syphilis.
Moreover, even assuming non-determinism, there seems to be no assumption that the probability that one should assign to the event ‘Smith gets paresis’ given the best information about the state of affairs after he got syphilis was the same as the probability assigned on the piece of information ‘Smith gets syphilis’.
Similarly, in the case of regular dice, there is no assumption that the dice is indeterministic, let alone that given the state of the universe, say, after the dice began rolling, the best probabilistic assessment to a 6 was 1/6.
b. The situation seems to be different in the case of hypothetically indeterministic QM, in which there simply is no better probabilistic assessment, and given the state of the universe before the decay (or any other event), such event was improbable, or very improbable, in a sense of propensity (side note: I admit I have some difficulty understanding this idea of probability as propensity, but I’m granting it here).
On that note, one may consider some of the traditional examples used in arguments against uncaused events, or in favor of explanatory principles like the PSR.
For instance, one example would be that bricks do not pop up in midair for no apparent reason.
But let’s say that we saw just that; i.e., let’s say that we saw bricks that pop up around us.
Someone might offer, as a proposed explanation, that they have some probability z > 0 of forming via some quantum process (e.g., tunneling), so that would allegedly explain it.
One can construct even more extreme situations, in which, say, bricks only pop into existence over the head of a person of religion X, hitting them in the head and causing injuries and sometimes even death. Someone might still propose explanations such as the previous one.
Would those be reasons, and so contradict the assumption that they popped out for no reason?
But moreover, it seems to me that even without knowing QM, someone might posit, as an explanation of why bricks just pop up into existence in mid-air (or even only over the head of a person of religion X, etc.), that the universe is such that it has some propensity for such events to occur, and perhaps even that in that case, the universe would be a cause of the bricks as well.
Yet, if bricks were to pop into existence around us like that, and, say, some scientists or philosophers proposed such explanation saying that no better explanation is available (as in the case of indeterministic QM) intuitively I would say that those scientists or philosophers failed to explain why those bricks are coming into existence like that.
That said, if one assumes for the sake of the argument that such proposed accounts would explain the phenomena in question, then it seems to me that even the common examples of events intuitively absurd that would allegedly happen if things could come into existence uncaused, or if things could come into existence without an explanation, etc., would not clearly be examples of things coming into existence uncaused and/or coming into existence without an explanation, since there would always be some potential explanation in terms of some propensity of the universe, etc.

Alex,
I understand you want to know how the many minds interpretation deals with cases where according to the Copenhagen interpretation there is, say, a probability 1/3 to observe one outcome and 2/3 to observe its complement. Well, even assuming the superposition of infinitely many minds (I understand this issue is not settled) here is a way to define a picture of reality which avoids the problems you suggest: The infinite set of superposed minds is an ordered one, where each mind in a position divisible by 3 observes the first outcome, and every other mind observes the second outcome. (There is also a solution for the case that the probabilities are irrational numbers: Nature probabilistically fills each slot in the ordered set.)
I claimed that there is no way to be a physical realist about QM without assuming that the world is absurd. The Copenhagen interpretation entails that physical reality becomes concrete only by the process of conscious observation, which is of course anathema to the materialist. But even if one is a substance dualist the Copenhagen interpretation implies some absurd things, for example that the decision of how to observe a photon emitted by a far away star which happens to lie behind a gravitational lens affects what that photon did billions of years ago billions of light-years away. (See Wheelerâs delayed choice experiment, for example here).

Alexander, I tried to post a long reply but my post apparently didn’t get through, and I don’t have a copy of the message I tried to post, so it seems to me it’s been lost. I’m trying a much shorter reply now.
1. Do you have a source or argument to that conclusion?
Some interpretations do not posit a collapse at all (e.g., Many Worlds, Bohm), and do not seem to have a problem with Bell’s theorem.
2. I don’t know who said it. Do you have a source, so that I can take a look at the context better?
In any case, that would still result in several problems. Briefly, and for example:
a. If the scenario you propose is one in which there was no decay before the first conscious beings, it seems we would have no good reason to trust our measurements about the age of the Earth, rocks, the beginning of life, etc., or even what happened on Earth before multicellular organisms, since we don’t know whether some conscious aliens in other planetary systems were making measurements that would cause radioactive decay on Earth before there was any life on Earth, and it’s not clear that unicellular organisms are conscious.
b. On the other hand, if when you say that the superposition state is tied to different decay times, those times are meant to be before there were conscious organisms and they were caused by conscious organisms, then that would require time backwards causation. But without good evidence of that, then there would seem to be no good reason to trust our measurements of the age of the Earth, the beginning of life, etc.
3. The post I tried to post earlier was mostly dedicated to address your points on this matter. I will try again later.

On further thought the ontology of the many minds interpretation appears not to be compatible with materialism. According to this interpretation reality consists of just what QM says, namely a superposition of all physical states of the universe according to the distribution of the universeâs wavefunction. But this is not a physical thing existing in space and time, but a mathematical object existing in the space of complex numbers. Albeit one where particular superposed states include the states of brains which produce experiences of the concrete physical values present in these particular states. And these experiences are the only concrete or âclassicalâ existents.
In short we have here a metaphysics according to which reality consists of just one mathematical object producing a myriad histories of concrete experiences. These include the experience of physical objects, but no physical objects, as such, exist. Thus, it seems, the many minds interpretation (or at least my understanding of it) works beautifully from the point of view of the scientific realist, but on the other hand rejects materialism.
What is the difference between the many minds interpretation and my Berkeleyan interpretation of QM? First, my interpretation substitutes the mathematical object with Godâs mind. And secondly, on my interpretation not all superpositions are actual but only one becomes actual, as decided by the mind of God and co-decided (within the physical limits of creaturely freedom) by the mind of created persons like us humans. So itâs not a particular mathematical object (the universeâs wavefunction) which produces a myriad histories of conscious experiences, but Godâs and our mind which produce one history of conscious experience. It is obvious that the Berkeleyan interpretation is far simpler and also entails purpose and intelligence, as contrasted with the brute and extravagant nature of the many minds interpretation. And comports naturally with the concepts of personal identity, freedom of will, creativity, and personal responsibility of creatures â whereas the many minds interpretation makes a joke of them, or rather, strictly speaking, eliminates them. Further, it describes how Godâs special providence, as entailed in classical theism, obtains. And, finally, contrary to the many minds interpretation it avoids the existence of histories which entail absurdities.

Matthew, thank you for the tip. I just registered.
Alexander,
Just a bit more on point 1. Roughly, Bell’s theorem rules out local hidden variables, but as far I I know, probably Bohr’s original interpretation and some modern views posit neither local hidden variables nor an ontological interpretation of wave function collapse (e.g., see the Wikipedia entry on the Copenhagen Interpretation, point 4.)
But I was just considering options, so I’ll leave epistemic interpretations aside for the sake of the argument.

Thanks for all the good comments.
The conversation has its genesis, I think, from the proposal that psr provides a good account of why recombination can’t result in a GR scenario–of why the impossible GR scenario is not a neighbor of a possible scenario. I should emphasize that those who doubt psr will not accept that proposal, of course; reasonable disagreement is expected.
But I’d like to comment on the argument for psr that Angra mentioned — that psr accounts for why (say) bricks don’t come to be in mid-air for no reason. The argument, as I think of it, need not imply that such events *couldn’t* have a low-probability quantum explanation; it’s that such events would be more regularly observed if an explanation isn’t required, in part because a quantum explanation isn’t *likely* to lead to such events. It’s like if I regularly see a bird outside my window. It might be *possible* that the bird spontaneously comes to be because of prior quantum states; but that’s not a likely explanation (which may account for Angra’s intuition that he wouldn’t accept such an explanation if it were proposed).

Thanks for the reply. Personally, even assuming the psr (on which I actually take no stance), I would not consider it an explanation as to why there can’t be contradictory scenarios, but it seems we discussed the matter already.
With regard to the QM scenario, it seems to me you’re suggesting a distinction between large objects coming into existence because of prior quantum states, and not because of them (i.e., uncaused), but I’m not sure I get in which sense there would be an ontological difference between the two cases.
For instance, let’s say that the probability of an event E, according to some interpretations of QM is p (which, let’s say, is very low), and E happens.
How do you think the world would differ between a scenario in which there is a QM explanation, and one in which E is uncaused? For example, would there be a difference in the number of particles, amount of energy, the experiences of agents, etc.?

That’s a good question, Angra.
I’m inclined to think the difference may be in the presence of a causal relation, which I take to be ontologically primitive.I would not consider [psr] an explanation as to why there can’t be contradictory scenarios
I wonder about an explanation as to why the impossible GR scenario isn’t a “neighbor” of a possible scenario — such as one in which the attack time of a single GR differs by a mere second. (You may say that such neighbors are possible, or that their impossibility is explained by their “nearness” to the GR scenario.)
I suppose I wonder if psr violations are “modal neighbors” (of neighbors) of a GR scenario.
Perhaps we could pose “The Grim Reaper Question”, which is this: which, if any, situations differ from the GR situation in modally innocuous ways?

Regarding the causal relation, what I’m having difficulty seeing is how it may be that in one case there is a causal relation and in the other isn’t, unless there is a difference in particles, amount of energy, etc.
On the issue of the neighboring scenarios, I would say that whether a certain amount of time is ‘mere’ is a judgment that depends on the minds of the agent.
For instance, assuming that time is not rigidly discrete, it seems a possible entity E(n) could experience something like what I’ve experienced while writing this post but in 1/n seconds.
For sufficiently large n, a second would be experienced by E(n) as lasting longer than what it would be for one of us to experience, say, a million years (assuming it’s metaphysically possible that a way around aging is found and it’s possible to survive for that long, etc., or something like that, which appears very plausible to me), or a trillion years, etc.
If E(n) has a mind in any way similar to ours (just operating a lot faster), she would not consider a second to be ‘mere’, and two scenarios would not strike her as neighboring just because the difference is one second.
So, if there is a neighboring relation between scenarios and that does not depend on the type of mind of the entity assessing whether the scenarios are neighboring, it seems to me that temporal distances do not make scenarios neighboring.
On the other hand, if we’re talking about a neighboring relation relative to, say, normal human minds, I do not see why one should consider that the particular characteristics of human minds, or of normal human minds, would be a guide to metaphysical possibility, except in indirect ways that are not relevant to cases like the one under consideration (e.g., whether a certain amount of time is a little or a lot) like where, say, rigid designators pick properties of [normal] human minds, directly or also indirectly by picking whatever property normal human minds track, etc..(and in those cases, human minds do not play any privileged role or any role; rather, human minds (like the minds of cats, dogs, etc., or pretty much anything, with or without a mind) can be picked by rigid designators, etc.
Similar points can be made about spatial distances.
As for contradictory scenarios, personally, I see contradictory scenarios as failed scenarios in a sense, since one attempts to define a certain scenario (or, perhaps more accurately, a category of scenarios, since consistent scenarios are almost never fully specified), but ends up giving a contradictory definition, and given that, my impression is that any potential similarity between them and consistent scenarios is gone as far as I can tell.
So, even assuming that there is such thing as a neighboring relation that related to metaphysical possibility, I get the impression that contradictory and non-contradictory scenarios are never neighboring â though, of course, I’m using my own intuitions about neighboringness to make that assessment; it might well be that there is no such neighboring relationship, and even normal human minds differ in what looks ‘neighbory’ to them, so maybe some scenarios look like neighbors to you, but not to me, without either intuitions being any guide to metaphysical possibility…

On the other hand, if we’re talking about a neighboring relation relative to, say, normal human minds, I do not see why one should consider that the particular characteristics of human minds, or of normal human minds, would be a guide to metaphysical possibility, except in indirect ways that are not relevant to cases like the one under consideration (e.g., whether a certain amount of time is a little or a lot) like where, say, rigid designators pick properties of [normal] human minds

Upon further consideration, that does not look right, since it might be that at least in some cases, ‘a short time’ may be used to talk about a time that is experienced in some way by normal humans, or similar minds, but even then, that would only play a role in whether it’s possible for amount X of time to be a short time, etc., not only the possibility of scenarios that look neighbory to humans on the basis of temporal (or spatial) distance.

Angra:
“it seems we would have no good reason to trust our measurements about the age of the Earth, rocks, the beginning of life, etc., or even what happened on Earth before multicellular organisms, since we don’t know whether some conscious aliens in other planetary systems were making measurements that would cause radioactive decay on Earth before there was any life on Earth, and it’s not clear that unicellular organisms are conscious.”
I guess you’re right. On the view in question, prior to the advent of consciousness, there was just a massive superposition, so it’s not technically correct to talk of there being rocks, cells and the like at that point. Rather, there are superpositions of different global configurations, some of which includes rocks and cells, and others of which don’t. So this would indeed undercut some of geology and evolution. Interesting indeed, and I can now see why it might well be problematic.

Alexander,
It seems to me that another potential difficulty is how one gets out of the massive superposition in the first place. I mean, in the massive superposition, there are no conscious living organisms. So, how would they come into existence?
I suppose someone might say that a powerful creator places a soul in some organism that didn’t have one before. But apart from the ontological commitment to the existence of such being, that would seem to require that there were organisms without souls before, rather than a massive superposition.
So, it seems to me that in any case, a creator might end up having to do a measurement, under those assumptions (i.e., collapse of the wave function as a real phenomena, and a requirement of consciousness in the observer that makes it collapse). And if someone is willing to posit a creator making one measurement, then I suppose they might as well also say that before there were conscious life, the creator was the one making all of the measurements, so there was decay, etc., and then geology and evolution work.
But that would posit an observer that is not describable by the rules of QM (unless the creator is also so described, but that too raises other issues), which is one of the reasons some versions of the Copenhagen interpretation were criticized (i.e., the observers they posited weren’t described by QM, though they weren’t creators or even required to be conscious).

I’ve been thinking about some of the different GR scenarios, and while my assessment on the matter remains that they don’t work, given the disagreement and different views on the matter, I think it might be useful to consider some parallels between GR arguments, and their connection with different theories about time.
My suggestions at this point would be:
1. If the GR argument works against the conjunction of an infinite past and the hypothesis that time is possible dense, then it works against the hypothesis that time is possible dense (i.e., the infinite past is not needed), since one can argue as follows:
Reasoning similarly as in the original GR argument, for some fixed time t0, between t0+1/(n+1) and t0+1/n, (1/n is always seconds), a reaper GR(n) is produced, and GR(n) is programmed to do the following task between (1 minute + t0+1/(n+1)) and (1 minute + t0+1/n)):
a. Check whether Fred is alive.
b. Do nothing if he’s not.
c. Kill him before the end of the interval in question if he is.
Then, stipulating that nothing else kills Fred, a contradiction arises just as in the infinite past case.
2. If the GR argument works against the conjunction of an infinite past and the hypothesis that time is discrete in an Aristotelian sense, then it seems plausible to me that it also rules out infinitely many angels in a finite past, even if those are angels who cannot have causal influence on the same place in spacetime, since one can mirror the GR argument against an infinite past on the assumption that time is discrete in an Aristotelian sense as follows:
Each angel (say, Angel#n) might decided at some time prior to the year 2114, that between t0+1/(n+1) and t0+1/n (where t0 is some fixed time in 2114) she will assert (maybe to herself; there is no need to say it out loud) “My name is [name of Angel#n]”; then, she does what she’d decided, and that contradicts the assumption that time is discrete in an Aristotelian sense.
A potential way out might be as follows: There possibly are infinitely many actual causally isolated realms, each with finitely many angels in it, and also infinitely many separate ‘times’, one for each such realm. But that might have its own problems (and it’s not clear to me that it would be proper to say that time is discrete in an Aristotelian sense; more precisely, each of the infinitely many times would be discrete in an Aristotelian sense).
3. If the GR argument does not work in 1., it does not work against things coming into existence without a cause.
If the GR argument works in 1. but not in 2., the GR argument against things coming into existence uncaused does not seem to work, either, since in that case, time is not possibly dense, and if time is Aristotelian-discrete (if it’s rigidly discrete, all GR arguments fail), then the reasoning against things coming into existence uncaused would plausibly be similar to the reasoning in the argument in 2.
On the other hand, if the GR argument works in both 1. and 2., then it seems to me it plausibly works against things coming into existence without a cause as well.

Angra:
I am not sure I’m convinced by argument 1, because on the Aristotelian assumption I am not sure that the kind of backwards supertask necessary to produce the GRs in such time intervals is going to be possible.
As for Copenhagen, my preferred version of it (I have no idea if it’s in the literature, though I would be surprised if it weren’t) would be that collapses so occur to prevent the formation of superpositions between physical substrates of a conscious state and states incompatible with the substrates of this conscious state, e.g., between a state of (a substrate of–I’ll omit this from now on for brevity) seeing a pointer in position A and a state of seeing a pointer in position B, but likewise between a state of the cat being conscious and alive and a state of the cat being dead.
Just as there is always going to be a tiny probability of my quantum leaping to the moon, there will always be a tiny (tinier, I expect) probability of a Boltzmann brain forming in the middle of a star (in a little pocket of brief liveability). But there will also be constant collapse, and since these probabilities are tiny, such Boltzmann brains are always (or the vast majority of the time–it does, after all, depend on how big the universe is) eliminated from the superposition before they form.
So, on this story, at some point it will like like there’s be about to be a superposition between a conscious and an unconscious state for the first time. Maybe we’ve got a superposition between a little fetal vertebrate and no fetal vertebrate, with the former having higher probability. As soon as (actually, “just before”) the little fetal vertebrate component develops enough for consciousness, collapse happens. Sometimes this will happen against the little fetal vertebrate and sometimes it will happen in favor of it. At some point in the history of the world it happened in favor, and so we had the first conscious animal.
You can then perhaps interpret this interpretation along the lines of Everett branching multiple worlds, except that consciousness prunes the branches, so that consciousness-facts are always constant between the branches. If so, then we can even say that before the first conscious animals, there were unconscious ones–though only in OUR branch.
But I’m just making stuff up. I haven’t worked out even a crude mathematical model (and I may not ever do it, because I don’t know much about philosophy of QM).

Alexander,
Regarding the Grim Reapers, in argument 2 I was mirroring the GR argument against an infinite regress of events on the assumption that time is discrete in an Aristotelian sense, and which also requires such supertask.
Assuming that your objection here (i.e., that you’re not sure that on an Aristotelian view of time, that kind of supertask is going to be possible) succeeds, then it seems to me that it similarly works against the GR argument against an infinite past on the Aristotelian assumption, since an infinite past on an Aristotelian assumption does not entail supertasks, so one may say that, perhaps, a reason to rule out all of the events happening together (in the GR argument against an infinite past) is that such supertasks are not possible, thus blocking the conclusion of the impossibility of an infinite past (personally, I think the reason it would be impossible is simply that that scenario is contradictory, but I’m assuming for the sake of the argument that that general objection to GR arguments doesn’t work).
On the other hand, if the objection that it’s unclear that such a supertask would be possible does not work against the GR argument against an infinite past on the Aristotelian assumption, I’m not sure why it would work against the argument against infinitely many angels on the Aristotelian assumption.
In short, the two arguments seem relevantly parallel to me.
As for the interpretation of QM that you suggest, if I’m tracking you right (which I might well not be; please let me know), it seems to me that the first collapse happens a very short time before the vertebrate in question develops enough for consciousness, and so there is collapse without consciousness (side note: I have no problem with that, and in fact that would also solve the other difficulty (i.e., for geology and some evolutionary theory), but I’m not sure you would agree with that).

Angra,
You ask about how the world gets out of the massive superposition in the first place.
My understanding of the Copenhagen interpretation is not that the world becomes real only when somebody makes a conscious observation and thus collapses the wavefunction. Rather the idea is that matter may exist in two quite different ontological phases: One where various physical states are superposed and thus various possibilities are open, and one where there exists only one physical state, no possibilities are open, and thus âconcretenessâ obtains. The evolution of the superposed phase obtains deterministically according to QMâs equations. And the transition between the superposed phase into the concrete phase is caused by conscious observation in this way: A deep property of matter happens to be that in particular configurations it express itself as consciousness. Further (as we know) consciousness exists only in one phase, namely a concrete one where no possibilities are open. Now consider the most complex but still non-conscious brain in the massive superposed phase of the universe. In exactly one physical state of the superposition some primitive event obtains which moves that brain in the consciousness expressing mode. Since that consciousness expresses that brain, and since that consciousness exists in the concrete phase, that brainâs phase loses its âmany possibilitiesâ property and instantly moves into the respective concrete phase. We call that sudden ontological phase transition âthe collapseâ of the superposed phase, or more commonly âthe collapse of the wavefunctionâ. This then would answer your question and describe how one gets out of the initial massive superposition.
So far so good. Now the interface between the phases of superposition and concreteness is a tricky one. For consider how things continue after the first appearance of consciousness: Since all physical change is governed by QMâs wavefunction the conscious brain quickly reverts to its superposed phase of many possible physical states (now all quite near to the initial physical state which expressed itself in consciousness). Many (but perhaps not all) of these superposed physical states of the brain are such that the brain will still express consciousness. Since consciousness can exist only in the no-open-possibilities concrete phase, exactly one of these physical states will become concrete (and the probability of it obtaining is governed by the well-known rule of Copenhagen which depends on the relative amplitudes of the wavefunction). This, incidentally, is how indeterminism enters physical reality. Thus there is a continuous âflickeringâ between superposed phase of the brain which allows for physical change and concrete (collapsed) phase of the brain expressed by consciousness, and which we experience as a smoothly changing conscious experience. (The flickering interval is presumably the time required for some state transition in QM, i.e the âPlanck timeâ of some 10e-44 seconds. No wonder we donât notice the flickering.)
A final point about collapse: When the consciousness expressing the brain transits or collapses from the superposition phase into the cocreteness phase, the phase of all matter which is logically entangled with the state of the conscious experience that has just obtained also instantly collapses to the corresponding concrete physical state. Thus, for example, consider the brain of a physicist watching the two measuring devices in a double slit experiment. When that brainâs superposition of states âI see the device to the left detecting the photonâ and the âI see the device to the right detecting the photonâ collapses into, say, the âleftâ possibility, then, instantly, the measuring devicesâ phase also collapses into the respective concrete state, namely the device to the left into the âphoton detectedâ state and the device to the right into the âno photon detectedâ state. And in turn these outside of the brain phase transitions render many future states of the universeâs wavefunction logically impossible. For example suppose the left device is connected to a cat killing machine. Unless some malfunction obtains the cat is killed after a few seconds, and all superposed states of the universeâs wavefunction where the cat is alive are rendered logically impossible. Thus, if you will, a bubble of collapse-like phase transitions will expand around the physicistâs brain into the rest of the universe. One may imagine physical reality as consisting of a many-possibilities haze being continuously âilluminatedâ into concreteness around the presence of conscious brains. A strange picture indeed, but one consistent both with the facts of QM and the facts of our conscious experience of our surroundings, and one much less strange than other interpretations of QM.
Now, interestingly enough, the above understanding of the Copenhagen interpretation makes some large scale testable predictions. Consider again the universeâs wavefunction before the appearance of the first conscious brain. This is a massive indeed superposition of myriads of physical state histories of the universe. In exactly one of these, the very âluckiestâ one, the first conscious brain will obtain thus starting the concrete history of the universe. And that state history is the âluckiestâ one in the sense that since the Big Bang it is the one physical state history where every single state transition allowed by QM happened exactly in the way that would produce at the earliest possible time a conscious brain. So whatâs the testable prediction? Suppose we had the means to compute at which probability a universe with our physical laws, physical constants, and initial conditions will produce a conscious brain. Then that probability should be extremely small. In other words, according to the above understanding of the Copenhagen interpretation, the probability of our brain obtaining in our universe should be practically zero. (Which, incidentally, is bad news for natural theology philosophers, since it predicts that the blind/unguided evolution of life obtains exactly as if an infinitely intelligent mind is guiding it.)
A second precise prediction would be this: We are the first intelligent brain in the universe. Thus the probability of conscious brains evolving earlier than the time our has evolved (i.e. some 13.7 billion years after the Big Band) is zero.
Unfortunately, we canât today compute the above probabilities, and it may turn out that it is infeasible to compute them. But there is a third prediction which we can easily test, and which has in fact obtained. Consider this: If it is extremely unlikely that the first conscious brain on some planet will evolve, then once it evolved there it will be some enormous time before it evolves elsewhere. Why? Because the universeâs history of state transitions is optimized for producing conscious brain in that one planet only. Thus when that first conscious brain (or its biological race after discovering technology) first looks around at the cosmos it will almost certainly *not* detect any signs of intelligent life elsewhere, since most likely conscious life wonât evolve elsewhere for a very long time to come. And thatâs exactly what we ourselves observe when we look around at the cosmos. The argument here is that the Copenhagen interpretation âexplainsâ why the cosmos appears to be so empty of signs of intelligent life. And indeed predicts that right now our young race is alone as the only intelligent race in the universe.
Conversely, the many-worlds or the many-minds interpretations is falsified. Here is why: Since we are here, we know that the universeâs wavefunction makes it possible for conscious brains to evolve somewhere. Now according to the mw or mm interpretations all possible world histories co-exist. If one randomly picks one world-history where consciousness has evolved, and randomly picks one conscious brain in it, then, very likely, that brain will be observing a universe full of signs of intelligent life. Why? Because it is unlikely that one has picked a brain in the very first planet where conscious brains evolved. Most consciousness including states of the universe for most of the time will be such that the cosmos is full of signs of intelligent life. But the cosmos we observe is not like that.

Dianelos,
My assessment above was based on what seemed to me like Alexander’s interpretation. As for the Copenhagen interpretation, it seems to me that there is more than one interpretation that goes by that name. If we’re talking about the original views of Bohr and Heisenberg, as I mentioned above, the former apparently considered collapse to be an epistemic matter (though he wouldn’t use the word ‘collapse’), whereas the latter did not use the word ‘observer’ in a usual fashion, and in particular, he did not believe it required consciousness (e.g., see the Wikipedia article on Copenhagen, where Heisenberg is quoted saying “Of course the introduction of the observer must not be misunderstood to imply that some kind of subjective features are to be brought into the description of nature.”
On the other hand, I see that the interpretation you have in mind â like Alexander’s â combines an interpretation of collapse in a non-epistemic way (say, an ontological way; I prefer not to say ‘realistic’, but I can go with that if needed), with an assumption that the observer needs to be conscious, though it has some differences from Alexander’s interpretation.
I may be missing something (if so, please clarify), but I still see it as problematic, for the following reasons:
1. Your scenario combines a complex non-conscious brain that becomes conscious in one state of the superposition. A question is: what causes the collapse?
If it’s the measurement by the conscious brain, then it seems to me that the conscious brain was part of the superposition prior to causing the collapse, but consciousness is said to exist without those possibilities (if I read your interpretation correctly).
If it’s something prior to consciousness, then it seems that consciousness is not required for the collapse in question.
Are you suggesting simultaneous causation?
2. There is still the problem for measurements of age of the Earth, the timeline of evolution, etc., before consciousness, since on this account, there was no radioactive decay before consciousness due to a lack of collapse.
3. You also seem to consider that human consciousness, or something like it, is required for collapse, so (for instance), insects, ancient fish, etc., won’t do. That would make the issue in point 2. even more pressing, since it seems that our measurements of age based on radioactive decay should not be trusted before there were humans (or similar beings), so that would take out most of geology and evolutionary history; granted, some other entity might be making measurements, but there is no good evidence of that, either, so it seems to me that our science would be seriously undermined.
That aside, I don’t think that we have good evidence that we’re alone in the universe. We have not made any attempt that would detect technological civilization with our level of technology but which is not trying to communicate with us (for instance), even in nearby stars (perhaps, in the closest ones, but not beyond that), and that’s only in our galaxy. If there advanced civilizations in other galaxies, we would not have detected them.

I’m having difficulty seeing is how it may be that in one case there is a causal relation and in the other isn’t, unless there is a difference in particles, amount of energy, etc.
Which perhaps translates into a difficulty with seeing how causation could be ontologically primitive (and non-supervenient upon non-causal properties). Well, either way, I suspect the “~psr implies macro chaos” argument ultimately turns on a Bayesian argument that contains a premise something like this: arbitrary (chaotic) macro events are less likely on some suitably general principle of explanation than on its denial. I wouldn’t think this argument would turn on whether such macro events could have low-probability explanations in terms of prior states. The plausibility of the premise may depend in part upon one’s assessment of the plausibility of alternative explanatory principles (and in part on whether one thinks quantum mechanics provides independent evidence against psr).
I’m going to have to keep thinking about your points about contradictions. I find it strange that a change in attack time of a single GR would make a modal difference (as when one of the GRs instead attacks first). But there are cases where small changes would seem to make a modal difference. For instance, suppose two simples cannot be co-located; then slight differences in location results in modally different situations. Of course, we can *explain* why in terms of the impossibility of co-location. But of course, regarding GRs, an explanation could be given in terms of the impossibility of contradictions. That explanation doesn’t seem satisfying to me, but it deserves thought.

Angra,
QM can be interpreted epistemically, namely as what we may know about physical phenomena. On this view âcollapseâ refers to the collapse of not-knowing. But, I take it, we are here concerned with a different question: Both the properties of our experience of the world and of the structure of QM, are factual givens. And they are produced by the same reality. The ontological (or realist) question then arises: Given these facts what should one reasonably believe about how reality is? And in particular, what should one believe if one assumes physical realism, namely that both these givens are grounded exclusively in a reality that has a physical/mechanical nature.
Now clearly on ontological Copenhagen âobservationâ must be understood as âconscious observationâ. An unconscious measuring device doesnât collapse the wavefunction since it is a physical system which is completely described by QM, and there are no wavefunction collapsing events in QM. On QM the unconscious measuring device will remain in a superposed phase until observed. (On the other hand nothing changes in our own observation of phenomena should it be the case that the measuring device is conscious and does collapse the wavefunction. After all, the wavefunctionâs collapse does not produce any visible traces.)
As for the numbered issues you raise:
1. What causes the collapse of the superposed phase of the conscious brain? The relevant properties of conscious experience. In particular the fact that conscious experience only exists in the concrete phase. And also the metaphysical necessity whereby concrete conscious experience is grounded in a brain having the respective concrete physical state. This is I suppose a case of âsimultaneous causationâ. One could also say that a physical brain in the superposition phase, by having one of its superposed physical states express consciousness, causes all other physical states to disappear and thus collapses into that one concrete physical state.
Please observe that this one-to-one relationship between concrete consciousness and concrete brain is not a logical necessity, but is entailed by the metaphysics of the Copenhagen interpretation. One can certainly conceive of a brain maintaining its superposed phase while one or more of its superposed physical states express themselves in the respective states of consciousness. No collapse happens. But then we have one brain expressing several different states of consciousness – and this is the metaphysics of the many minds interpretation.
Strictly speaking then, itâs not correct to hold that on Copenhagen the conscious brain by observing the result of a quantum experiment collapses the experimentâs wavefunction. Rather the very presence of consciousness entails the collapse the wavefunction of the brain which expresses that consciousness. As I described in the previous post, the collapse of the experimentâs wavefunction happens concurrently but is ontologically secondary. Or, if one insists in using the concept of âobservationâ, the conscious brain is really observing its own physical state, not the experimentâs.
2. About measuring the Earthâs age. Consider again the massive superposed phase of the universe before consciousness evolved. Time is still flowing, and radioactive atoms are still decaying, albeit in a superposed state. Thus at any point in time a radioactive atom exists in all possible physical states of âdecayedâ and ânot decayedâ, albeit the wavefunction defining the probability distribution among these states varies with time. Suppose now that at some later point in time a conscious being comes close and an observation collapses that particular atomâs wavefunction into one concrete state, namely either decayed or not decayed. According to QM, if the age of that atom at that particular point of time (i.e. the time since the atom was formed) is one half-life then the probability of it collapsing into the decayed state is 1/2. If the age of that atom is two half-lives then the probability of it collapsing into the decayed state is 3/4, and so on. Thus, the physicist measuring the concrete states of a large number of such atoms in her specimen will be able to estimate its age. For example if 3/4 of the atoms observed are found in the decayed state then the specimenâs age is two half-lives. Similarly, all scientific methods to measure age based on radioactive decay will work well. I donât see any problems here, and certainly no God making observations is needed.
3. I am not assuming that human consciousness is required for collapse. What I wrote in the previous post refers to physical states which express themselves in consciousness, and which for brevityâs sake I called âbrainâ, and for simplicityâs sake often used as referring to a human brain. But any conscious brain collapses its own wavefunction. I have also discussed the wavefunction collapse of the very first conscious brain. That collapse is special only in the sense that it is determined since the beginning of the universe, whereas all later wavefunction collapses are indeterministic. Now we know that human brains are conscious, we assume that brains of mammals are also, but perhaps even the brains of insects are conscious.
(If the above Copenhagen interpretation is correct then hereâs in principle a way to discover which types of brain are conscious, and indeed which was the first type to become conscious: Start with some very simple type of brain, such an insectâs. Compute the earliest possible time t1 in which in our universe a brain of the complexity of an insectâs will evolve. Further find out the time t2 in which in our universe insects did evolve. If t1=t2 then insects are the first conscious beings (for the actual history the world is optimized for producing the first consciousness). If t1

Joshua,
I’m not sure how to make a Bayesian assessment of the probability of what you describe as chaotic macro event on the denial of the psr.
More precisely, I think it depends on background conditions (e.g., some non-deterministic but constraining laws, etc.). Also, assuming either determinism or that the psr is compatible with indeterminism (I’m not sure how, though), a more modest principle like no uncaused events in any world branch able from our own would result in the same observations, so there is no need to commit to a general claim about all possible worlds.
Granted, someone might ask for an explanation of why it’s not possible in worlds branchable from our own; a reply might be in terms of the causal structure of the actual world. On the other hand, if someone posits the psr, someone might still ask for an explanation as to why it’s true.
I’ll keep thinking about your points as well.
Regarding changes in one single entity (e.g., removing one entity, reprogramming it), I don’t find that too odd, personally.
An
Only a supereaper can kill a reaper, and nothing kills Fred unless a reaper kills him. Reapers and superreapers do not fail. Also, Fred does not resurrect.
So, there is only one reaper GR1, set to kill Fred between noon + 1 second and noon + 2 seconds. At noon + 20 minutes, Fred drinks some wine. There is also only one superreaper, SGR 1, programed to kill GR1 between noon + 1 nanosecond and noon + 2 nanoseconds.
So, S1 is not contradictory. But if S1′ is like S1, only removing the superreaper or suitably changing its programming, it’s contradictory (we can set up scenarios in which changing the programming one nanosecond (for instance) results in a contradiction).

Dianelos,
Regarding the epistemic interpretation of the collapse, I was not referring to epistemic interpretations of QM as a whole; for instance, Bohr seemed to interpret collapse epistemically, but he too had an ontological interpretation of QM.
As for ontological interpretations of the collapse, as I pointed out, Heisenberg did not understood as ‘conscious observation’. On the contrary, he denied that. His view is criticized (and is no longer endorsed) because he treated the observer classically (so, the observer was not describable within QM), but not because he didn’t posit conscious observers.
If you take a look at Weinberg’s criticism of the Copenhagen’s interpretation (what he calls “the” Copenhagen interpretation, anyway), he states that it’s “surely wrong” to posit observers not describable by QM, and also claims that “considerable progress” has been made towards resolving the problem.
I have to admit that I’m not qualified to directly assess the level of progress (but if you have a link to a source backing up your position, please let me know), but what seems to be clear is that present-day interpretations of QM based on an ontological collapse of the wave function neither exclude the observer from QM nor claim that the observer needs to be conscious.
On the points you raise:
1. I would say that the Copenhagen interpretation, in its original form (based to a considerable extent on Heisenberg’s view), did not posit a conscious observer as far as I can tell. If by “Copenhagen Interpretation” you mean some specific version of what is usually called that, please let me know which version.
But leaving that aside, and on the substantive points, the view you propose is at least committed to simultaneous causation, which might be problematic.
There seems to be another difficulty, related to that. You say:

One could also say that a physical brain in the superposition phase, by having one of its superposed physical states express consciousness, causes all other physical states to disappear and thus collapses into that one concrete physical state.

I might be misreading, but I get the impression that at some time t0, the conscious state would be superposed with non-conscious states (right before the collapse happens). I thought that that was not compatible with your take on consciousness existing in one phase only. Please clarify.
To put it in a different way: assuming for the sake of the argument that time is not dense or the past infinite, it seems that last (or latest) time t0 at which there is no consciousness, and a next time t0+e at which there is consciousness.
If the conscious state at t0+e is superposed, then consciousness can exist not only in one phase, which seems to be against an assumption (if I understood your theory in your previous post).
On the other hand, if the conscious state at t0+e is not superposed, one may ask what caused the change from a superposed state at t0 to a non-superposed state at t0+e; but it seems it can’t have been consciousness at t0+e, since it’s a change from a state at a time t0, which is past relative to t0+e.
I’m not sure how consciousness, which only exists at t0+e, might cause a collapse from a state at t0.
2. On ontological interpretations of wave function collapse, radioactive decay seems to require collapse, and then half-life values would be false before the first collapse, since it’s not the case that a number of atoms would have decayed, etc. That’s why this would be a problem, since we wouldn’t be able to use radioactive decay to measure times before that first collapse, and that first collapse wouldn’t seem to suggest that a huge number of the atoms that existed before without decaying would decay at once or in a very brief time (which would also make half-lives false at those times) making it look just as if they had been decaying at the rate we know, thus making our estimates of the age of the Earth, rocks, etc., work.
At the moment, I don’t see any solutions to those problems.
3. Okay, thanks for the clarification.
So, that would resolve the problem, perhaps, since the time of multicellular life, but not beyond that, since unless there is good reason to think that unicellular organisms are conscious (and I doubt that, unless panpsychism is true, but if it is, then conscious organisms are not special, either), then it seems also that our measurements beyond the time of multicellular organisms (at least, in some planet; we wouldn’t know when) would not appear to be reliable.
Regarding the method for testing whether a type of brain was the first to become conscious, I think the problems would be that:
i. We wouldn’t be able to trust our assessment of age beyond a certain point, and that would mess with the whole process.
ii. We don’t know on which planet there were brains as complex as those of insects first.
On the issue of the argument for being alone, there is a lot of room for discussion, but briefly:
a. The argument would seem to at most show that there are no other beings with the intelligence of humans. It wouldn’t rule out unicellular organisms, or things as complex as, say, insects. If there is no assumption that humans or something like that are required for consciousness, then a lack of advanced civilizations wouldn’t rule out consciousness elsewhere, so
b. I think the argument from the lack of colonization has some force when it comes to our galaxy, though it’s not conclusive in my view (there are potential reasons why advanced civilizations might not be spreading so quickly).
c. On the other hand, I think it’s much weaker when it comes to potential civilizations from other galaxies, since (among other issues):
i. It’s not clear that that intergalactic travel will ever be doable. It might be, but it’s not clear at all that it will be, and getting enough energy for intergalactic travel is a serious problem (Eventually, the Andromeda galaxy will merge with the Milky Way, but that’s not the same thing).
ii. Even if intergalactic travel is technologically possible, given the expansion of the universe, it seems plausible that only a very small fraction of the observable universe will ever be colonized by our successors. The same would apply to other civilizations in the observable universe.
iii. The universe may well be much bigger than the observable universe.

Regarding changes in one single entity (e.g., removing one entity, reprogramming it), I don’t find that too odd, personally.
An
Only a supereaper can kill a reaper, and nothing kills Fred unless a reaper kills him. Reapers and superreapers do not fail. Also, Fred does not resurrect.

Sorry, that should read:
Regarding changes in one single entity (e.g., removing one entity, reprogramming it), I don’t find that too odd, personally.
On that note, we may consider scenario S:
Only a superreaper can kill a reaper, and nothing kills Fred unless a reaper kills him. Reapers and superreapers do not fail. Also, Fred does not resurrect.

Angra,
Clever. Here’s a simpler case: S1 = “Fred drinks wine at noon and is destroyed forever by a reaper one minute later”, and S2 = “Fred drinks wine at noon and is destroyed forever by a reaper one minute earlier”. They differ by a single attack time, yet only one results in a contradiction.
In this case (as in yours), there is no temptation to think that Fred’s time of drinking is recombinable with different attack times, since his drinking time depends upon the attack times. In the GR case, by contrast, what’s needed is that different individually possible GRs are recombinable (where the difference between them is only a difference in intrinsic powers). And that type of recombinability is, to me, very tempting.
(Of course, even if the powers are jointly possible, it doesn’t immediately follow that they can be jointly exercised. Still, I wonder why a power can’t be exercised in a situation. It seems plausible to me that the answer will be because something in the situation blocks it–and not merely logic.)

Joshua,
Very interesting points. I think I see what you’re saying. My take on that is more or less as follows:
If we’re talking about why something cannot happen at the actual world or a world branch able from it, then the question of why it can’t happen (causally) plausibly has an answer. In that case, the actual conditions determine what will prevent it.
But let’s consider a hypothetical scenario in which there are, say, infinitely many unembodied beings {U(n)} in a finite past. That scenario, unlike the actual world, is underdetermined.
Perhaps, more than a “scenario”, to be more precise we should say that the conditions in question (i.e., our description of the scenario, in this case that it has infinitely many unembodied beings in a finite past)
So, what prevents each of U(n) from checking whether Fred is alive, etc., resulting in contradiction?
I would say that what prevents them from doing that varies from one scenario in that category to another scenario in that category. There are infinitely many causal structures compatible with the conditions of the scenario (maybe in some scenarios, it won’t be even that something prevents them from doing that; they just don’t do that; still, if you find that to be implausible, then I would still say that what prevents them plausibly varies from scenario to scenario, even if in each of them something prevents them).
The same goes for an infinite past scenario. Assuming it’s not contradictory after accounting for the meaning of words including rigid designators, I would say plausibly it’s a possible scenario (or a category that contains possible scenarios), because that’s what I think the question of possibility in this context plausibly is about (but there might be some miscommunication going on; that might explain some of the apparent disagreement), but what would prevent them from performing a task that results in a contradiction depends on the scenario.
In some such scenarios, they’re too far apart from each other and the speed of light is a limit. In some other scenarios, they don’t live for long enough for there to be more than finitely many of them alive at once, etc.
So, a single causal answer is not available, unlike the case of the real world. There is still the answer that it’s not possible because it’s contradictory. That’s fine in my view, but it does not suggest logic is somehow blocking their actions. Granted, someone might ask for an answer that is neither causal nor ‘logic prevents them’, either. But I don’t know how that might be, or why such an answer would be useful.
Side note: assuming that you conclude that my answer above is not satisfactory and that the GR argument rules out temporal density, I’d like to ask your take on what would prevent infinitely many unembodied beings in a finite past from exercising their powers, in the following way: UB(n) asserts to herself “I like the number n”, between noon+1/(n+1) noon+1/n? .
If the answer is that time is not possibly dense and that blocks it, it seems to me that the same reply could successfully be given to other GR scenarios, like the one involving an infinite past or things coming into existence without a cause.

Apologies for commenting without finishing reading the comments. But the basic grim reaper argument doesn’t seem to depend upon the infinity of the past so much as the infinite possibility of the past. Time, as far as we know, is infinitely subdivisible anyway and the world seems pretty complicated at all time (and size) scales. So it is perfectly conceivable for there to be a GR factory which has existed for the whole finite past of the Universe, creating GRs more slowly as time goes on, with one GR created at each moment 1/N, and slated to kill Fred at 12:30 – 1/N if Fred’s death isn’t already guaranteed by a previous GR.

Heisenberg, like others in his time, interpreted QM by dividing the world into quantum and classical regions. I agree with Weinberg that this is wrong. QM governs all physical systems; indeed quantum effects have been produced in the laboratory in one ton heavy crystals. And QM describes all physical systems (whether a measuring device or a human brain) as a wavefunction of a superposition of many different physical states. But when we actually look the measuring device is showing only one concrete result â either that the photon has passed through the left or through the right slit. Therefore, in order to understand our conscious experience of a concrete world, the appropriate interpretation must be added to QM. And, prima facie, since QM already says all that is to be said about physical systems (QM is assumed to be a complete theory), what is added must be non-physical and intimately related to the conscious experience we try to understand. Hence the idea that conscious experience (the âobservationâ) must be collapsing the wavefunction into one concrete state. It is true though that later other non-collapse interpretations have been proposed according to which itâs not the wavefunction that collapses into one state but our mind or even our brain that explodes into many states. Indeed when Weinberg speaks of âconsiderable progressâ he probably means his favored many worlds interpretation (according to which the entire universe including our brain is continuously being split into a vast number of parallel versions). But Copenhagen is a paradigmatic collapse interpretation.
You ask for sources. There is a huge list of quotes by eminent physicists who insist that the way to understand QM is by assuming the primacy of consciousness, or even that physical attributes are âcreatedâ by consciousness (you can read a collection of them in my review of Victor Stengerâs âQuantum Godsâ). A quote by physicist David Mermin comes to mind: âWe now know that the moon is demonstrably not there when nobody looksâ. There is even a mathematical proof by von Neumann in his Grundlagen, where he demonstrates that the idea of physical primitives having by themselves concrete attributes is incompatible with quantum theory. Thatâs why von Neumann is regarded by many as âthe godfather of the consiousness-created reality schoolâ. Incidentally the best book I know about the problem of realist interpretation of QM is Nick Herbertâs âQuantum Realityâ (the quote about von Neumann is on page 47). Whatâs certain is this: QM is one of the very greatest intellectual discoveries of all time, and the metaphysical implications of it are momentous, one way or the other.
Now your comments on the timeline of the actual collapse are incisive. Let me try to explicitly describe the in my judgment best realist understanding of Copenhagen using small time increments âeâ, which would be the smallest increments that produce any change. I will use the brain as the physical system where collapse obtains, and without loss in generality I will use only a very small number of superposed states.
Letâs first consider the case of the first brain becoming conscious. At time t=0 the complex but still non-conscious brain B exists in the superposition of two physical states s1 and s2
t=0: B(s1), B(s2)
According to the deterministic evolution of the wavefunction at time t=0+e state s1 evolves into states s11 and s12, and state s2 into states s21 and s22. All these physical states are complex but still not of the complexity required for consciousness. So at t=0+e the brain still exists in the superposition phase of four states:
t=e: B(s11), B(s12), B(s21), B(s22)
Now at t=0+2e something special happens. One of the new physical states of the brain defined by QM is such that it expresses consciousness. Letâs assume that this state transition is the s21 -> s211. Thus now a new kind of ontological entity enters reality namely the consciousness expressed by that state: C(s211). But since on Copenhagen it is metaphysically necessary that a concrete consciousness is expressed by the respective concrete brain, the ontological phase of the brain âcollapsesâ from being a superposition of many different physical states into one state B(s211). So here is the picture of reality at t=0+2e:
t=2e: B(s211), C(s211)
Now letâs see how reality continues to evolve after consciousness has entered the picture. QM defines the evolution of physical systems and says nothing about consciousness. Letâs suppose that according to QM state s211 will evolve into 3 new states: s2111, s2112, s2113. Letâs further suppose that only s2111 and s2112 are of consciousness expressing complexity. S2113 describes the physical state of a non-conscious brain. Since on Copenhagen metaphysics consciousness cannot exist in a superposed state, C(s2111) and C(s2112) cannot coexist. So nature is forced to choose one physical state. On the naturalistic view nature does this blindly by throwing dice and picking one of the three states (while respecting the respective amplitude probabilities of the three physical states). Suppose these probabilities are 0.6 for s2111, 0.2 for s2112, and 0.2 for s2113. As luck would have it the consciousness expressing state s2112 is indeterministically chosen. (Had s2113 been chosen then the brain would transit back to a non-conscious state.) Thus here is the picture of reality at t=0+3e:
t=3e: B(s2112), C(s2112)
We see that brain and mind states will remain concrete and identical for all future.
One could also describe a less granular picture of reality, where once consciousness enters the picture the world passes though a sequence of collapsed and uncollapsed states (the âflickeringâ picture I spoke of earlier). This picture is more consistent with the intuitions of those who embrace the PSR, since there is always a real reason that causes the next state of reality. For clarityâs sake I identify with an â*âall physical states which are consciousness producing:
t=0: B(s1), B(s2)
t=e: B(s11), B(s12), B(s21), B(s22)
t=2e: B(s111), B(s112), B(s121), B(s122), B(s211*), B(s212), B(s221), B(s222)
t=3e: B(s111), B(s112), B(s121), B(s122), B(s211*), B(s212), B(s221), B(s222), C(s211)
t=4e: B(s211*), C(s211)
t=5e: B(s2111*), B(s2112*), B(s2113), C(s211)
t=6e: B(s2111*), B(s2112*), B(s2113), C(s2112)
t=7e: B(s2112*), C(s2112)
At t=2e the first consiousness expressing physical state deterministically appears in the massive superposition of the universe. At t=3e the respective consciousness is expressed. Which at t=4e causes the collapse of the brainâs wavefunction into the respective concrete state. Driven by QM, at t=5e the brain again enters a superposed phase of three physical states, two of which are consciousness producing. At t=6e and given the prohibition of consciousness existing in a superposed state, nature randomly (but respecting QMâs distribution) chooses one of the three physical states. And, luckily for consciousness, it happens to choose the consciousness expressing physical state s2112. And that state is expressed in a new conscious states C(s2112). Which at t=7e collapses again the brainâs wavefunction. And so on.
Please observe that according to QM at t=4e the wavefunction still contains the 8 physical states s111..s222, and at t=5e it contains a still larger number of states. But according to Copenhagen even though these states exist in QMâs wavefunction, only a fraction of them survive in reality. And what causes that continuous push into a more concrete reality is the existence of consciousness.
In short one could write a computer program which would ârunâ the history of physical reality as well of our conscious experience of it following the deterministic rules of QM plus some random die throwing to decide the indeterministic future, once consciousness enters the picture. Thus there are no conceptual problems in Copenhagenâs description of reality. What bothers materialists though is that on this view what causes the pruning of all the possibilities allowed by QM into the concrete physical reality we observe around us is consciousness. What dualist theists on the other hand should very much like in this picture is that it creates logical space for both human free will and Godâs special providence to obtain, by having Godâs will affect the throwing of the dice in a way that comports with Godâs providential will and also with creaturely free will. There goes the famous interaction problem.
As for the issue of radioactive decay, it definitely does not require collapse. It seems your intuition tells you that decay is something that has or has not obtained. But thatâs not the picture QM gives. In the same way that on QMâs wavefunction an atom exists in two places at once, that atom also exists in the decayed and not-decayed states at once. Until that is we observe that atom, its wave function collapses, and we find it, say, in that place rather this place, and having decayed rather than not decayed.
Consider the timeline of 8 radioactive atoms. The superposed physical state of the atoms are described by (âX% not-decayed, Y% decayed). At t=0 the atoms are formed. For simplicity we shall describe only the superposed state of one atom, since the states of the other atoms are identical:
t=0: A(100% not decayed, 0% decayed)
t=1 half time: A(50% decayed, 50% not decayed)
t=2 half times: A(75% decayed, 25% not decayed)
and so on
Thus, for example, at t=1 half time all 8 atoms exist in the state 50% decayed and 50% not decayed. Now suppose at some point in time the 8 atoms are observed, their wavefunction collapses, and the following concrete states are found: 6 atoms have decayed and 2 havenât. This is consistent with t=2 half times, for at t=1 half time one would expect only 4 of the atoms to have decayed, and at t=3 half times one would expect 7 of the atoms to have decayed.
About the method for discovering which brains are conscious: As I have argued, if the Copenhagen interpretation of reality is true then it is probable that the first conscious brain evolved on planet Earth. Why? Because on Copenhagen the very earliest brain in the massive superposition of the universeâs wavefunction to become conscious collapsed the wavefunction and thus actualized that particular history of physical state transitions. And that history is the one where each single elementary event is such as to produce a conscious brain at the earliest possible time. But once the first conscious brain appears the universeâs history is not longer thus optimized, and on the contrary enters its indeterministic evolution. Thus the probability that fairly quickly other conscious brains would independently evolve on other planets in the universe appears to be low. For a long time the planet on which the first conscious brain evolves will be the only one where conscious life exists. Planet earth is a place where conscious life exists. Thus the very first conscious brain has probably evolved here, and there is no conscious (and hence complex) life anywhere else in the universe.
Now, please observe that the validity of above argument is not required for the method I described to work. If we compute t1 and measure t2 for the case of insects, and we find that t1=t2 then we have proof that the evolution of insects was the absolutely optimal one, and thus that the brains of insects are the first conscious brains to have evolved in the universe. T1 > t2 is logically impossible. And in all cases where t2 > t1 we donât have the earliest conscious brain. Thus by starting with the simplest and almost certainly non-conscious physical systems and slowly moving towards more complex brains until we find a t1=t2 we would discover which is the earliest conscious brain and also which is the minimum complexity required for consciousness. If we don’t find a t1=t2 then we have proof that, though improbable, consciousness has first evolved elsewhere. That method is theoretical of course.
As for the argument from the colonization of the galaxy I won’t defend it, since I happen to agree with you that there is a reason to believe that the human race (or any intelligent race) will choose not to colonize the galaxy. The survival of our race probably depends on wisdom (so weâd better get good philosophy education to the basic school curriculum), and one of the wisest things that have ever been said is that value is not grounded in quantity but in quality (or as the ancient Greeks put it âouk en to pollo to euâ). Which, incidentally, theologians discussing the attributes of God seem to overlook.

Dianelos,
I find expressions like ‘non-physical’ to be usually too vague for the purposes at hand. I would ask for a definition of ‘non-physical, or a way of distinguishing between the two. I would ask a similar question about ‘naturalistic’.
For now, I would say that, as far as I know.
1. QM is intended to describe the world around us at a low level, but not to split the world into categories like ‘physical’ and ‘non-physical’.
2. QM does not seem to describe gravity. Also, there may be other forces (e.g., the accelerated expansion of the universe may be the result of it). So, it may well be that it’s not a complete description, even at the level in question.
3. Granted, Copenhagen as it’s usually understood is a paradigmatic collapse interpretation, but not one that demands that the observer be conscious. Rather, Copenhagen traditionally makes the division between classical and non-classical systems.
4. Under an ontological interpretation of the collapse of the wave function, it seems to me that it would be implausible that the observer needs to be conscious. That would not only posit an odd kind of discontinuity in the world, but would be a problem for sciences like geology, biology, etc., which provide good accounts of many of our observations at a higher level, unless perhaps something like what you propose (if I get it right) is also assumed, but that would seem to imply, say, that the Moon isn’t there when no one is watching, or something like that (see below for more details).
Instead, I think an approach like what Weinberg suggests (see below) would be much better suited, again assuming an ontological interpretation of the collapse in question.
On the other hand, if the only reasonable way to interpret the collapse of the wavefunction ontologically were to ascribe consciousness to the observer â but many experts do not seem to agree -, I would take that as good (though defeasible given sufficient evidence, of course) reasons not to assume such an ontological interpretation.
5. Regarding Weinberg’s views, he does not seem to consider the Many World Interpretation satisfactory, though he rejects Copenhagen as well (e.g., see this paper entitled “Collapse of the State Vector”), in which he discusses precisely a number of theories about that issue.
Essentially, he suggests corrections that would include ontological collapse, but at all levels, not just at the level of measurement by a classical system as in Copenhagen.
That would be fit much better with a uniform reality, and it would be perfectly in like with geology, evolutionary theory, etc. (if that approach fails, though, there are still other interpretations that do not posit ontological collapse).
6. Thanks for the sources.
Your previous point was that clearly, on ontological Copenhagen “observation” must be understood as “conscious observation”. I take it you didn’t mean that in the sense of the traditional Copenhagen interpretation, since that one does not understands “observation” (or “measurement”) in that fashion but as something that involves a classical system, but rather, that you were saying that clearly, on an ontological interpretation of the collapse of the wave function, the observer needed to be conscious (but if I misunderstood what you were trying to say, please let me know).
While it’s true that some physicists have proposed that interpretation, it’s also the case that others have rejected it, and proposed alternatives. Given the previous considerations, I would be inclined to say that the most probable scenario is that either there is no ontological collapse, or it does not require consciousness, but I get that you don’t agree.
On the issue of your proposed interpretation, I don’t know that on Copenhagen it’s metaphysically necessary that a concrete consciousness is expressed by the respective concrete brain; Copenhagen does not seem to make claims about consciousness.
But that aside, under the interpretation you described, it still seems to me that the change from a superposed state at t=e to a non-superposed state at t=2e was not caused by consciousness (which didn’t exist until t=2e). But then, someone might posit also that there are other states (other than conscious ones) that do not exist in superpositions, and so there is collapse without consciousness.
As for radioactive decay, your proposal seems to me to suggest that until a human goes and, say, measures at the amount of C14 in some bones, there is no such thing as the amount of C14 in those bones, only superposition states, etc.
Essentially, that would get around the problem of decay before there was consciousness vs decay after there was consciousness by positing that in any case, there is no decay until we measure it (or rather, the states are superposed), and the decay rates do not actually apply when there is no observation (i.e., they shouldn’t be interpreted in an ontological manner; the particles had not actually decayed), and so there would not be a particular reason not to trust the measurements before the time of consciousness any more than after that time.
But the cost of that alternative would seem to be that the vast majority of the processes in the universe remain in superposition states, etc.; essentially, it reminds me of quote you mention âWe now know that the moon is demonstrably not there when nobody looksâ (i.e., it’s a number of superpositions, etc). I disagree with that view, but just to be sure: is that the picture of the world that you have in mind, or have I misunderstood?
Regarding the issue of which brains are conscious, as I mentioned, the Copenhagen Interpretation, as the term if traditionally understood and on the ontological version of collapse, does not posit any role for consciousness in the observer, so I will take your claim as a claim under the interpretation that you propose and which combines ontological collapse with a requirement of consciousness, the first conscious brain in the universe evolved on Earth.
As I mentioned above, the transition from superposed at t0+e to non-superposed at t0+2e does not seem to have been brought about by consciousness, but that aside, your proposal here seems to have the consequence that the evolution of other lifeforms elsewhere in the universe did not happen (i.e., it was just a massive superposed state) until that first brain became conscious here on Earth, which updated that particular history.
However, there are plenty of histories about what evolves on Earth that are compatible with evolution on many other planets, and there seems to be no good reason to think that the first consciousness somehow resets the whole universe, so to speak (technically, it would not be a reset since there would only be superpositions before that, but the point is there would be nothing suggesting things have to start from scratch elsewhere).
Let me put it in a different way:
Let’s say that the first conscious brain was lifeform X, on planet P. When the wave function collapses, there may well be all sort of non-conscious lifeforms elsewhere in the universe (say, {Y(n)}, for all n less than n0), and with different degrees of complexity (In fact, one seems more plausible than having considerable complexity in one place, and pretty much nothing elsewhere, but that assessment is not needed).
Also, there is no reason to think that they will take Y(n) and its species longer to evolve into something conscious than it took for X to evolve from something akin to Y(n) in terms of brain complexity to what it is at the moment of collapse.
In fact, given a sufficiently large universe, one would expect that some of those Y(n) would take more or less as long, others longer, and others shorter to make that evolutionary transition.
That aside, and regarding the method you propose, I don’t know how one would go about computing t1, but you said the method is theoretical, so I take it you don’t think it’s usable.

Angra,
Thanks. I suppose I would find it surprising that there *must* be a causal structure that causally blocks (or prevents in some way) the GR scenario (especially on your notion of logical necessity). As for what blocks (prevents) scenarios involving infinite temporal density, my answer is that no blocking (in terms of concrete factors) is needed if it isn’t even possible for all the entities in question to be produced (whether because of psr, no infinite past, no infinite events, or whatever).
The sticking point for me is that *if* certain causally and spatially disjoint things *can* co-exist exist, then I’d expect that any one of those things *could* be destroyed without thereby destroying the others (wouldn’t you?); and if things have certain disjoint powers, then I’d expect it to be *possible* for those things to jointly exercise their powers–except in situations where they are blocked by something (or each other).

Joshua,
Thanks for that reply.
Regarding whether there must be a causal structure (not the same in every scenario) that blocks or prevents each consistent scenario from turning into an inconsistent one, I wasn’t taking a stance on whether there has to be something. It’s not clear to me whether that’s part of the condition of non-contradiction. If it’s not, then there need not be anything.
But in that case, it seems to me that what you’re suggesting is that somehow being ‘impossible’ blocks the contradiction. I don’t know how to construe that, or why that would explain why the contradictory scenario cannot happen more than the fact that it’s contradictory.
In other words, let’s say that a proposed explanation of why some scenario S is impossible is that it’s in the category C of scenarios, and every scenario in that category is impossible (even if C does not contain only contradictory scenarios).
Then, some issues arise (for me, anyway):
1. Why would an explanation that some scenario T is impossible because it’s in the category C2 “contradictory scenarios”, and every single scenario in that category is impossible, not work as well?
For instance, if a proposed explanation is that contradictory GR scenarios are impossible because (say) temporal density is impossible and they involve temporal density, why would the reply that contradictory GR scenarios are impossible because contradictions are impossible and contradictory GR scenarios involved contradictions, not work just as well, without having to posit impossibilities without contradictions?
2. The idea of metaphysical impossibilities that do not involve contradictions even after considering meaning and rigid designators (unless there is some rigid designator lurking there, e.g., involving the term “time”) is problematic for me, since it leaves me wondering what’s meant by “impossible” and “possible” in this context.
More precisely:
a. If I’m considering the category of strictly logically impossible scenarios, I have intuitions about it in a broad sense of ‘intuitions’, namely I can check for contradictions. I conclude that scenarios in which, say, scientists got it wrong and water is not H2O are strictly logically possible.
b. If I’m considering the category of scenarios that are logically possible after considering the meaning of the words, including rigid designators, then assessing possibility is more difficult, but I still have means of doing so (intuitions in a broad sense of ‘intuition’), since I can use my intuitive grasp of the words to check whether there are rigid designators and then check for contradictions. Even without empirical evidence, it may be possible to tell that “Water is H2O” is possible if and only if it’s necessary.
Still, empirical evidence is needed to settle the matter (I’m counting evidence about the meaning of the words separately for convenience, but strictly speaking I think it should also count as empirical evidence)
c. If I’m considering the category of what’s possible in a world with the same past as ours, with the same entities and actual causal relations, I don’t have much in the way of intuitions. I would have to learn more about the entities that exist in our world, and there is the question of whether determinism is true, etc. But at least I can to some extent tell what I’m looking for (i.e., causal possibility in the actual world or worlds with the same past).
d. If I’m considering the category of what’s possible in a world with entities with the same powers as our world, the situation is similar to c. in terms of a lack of intuitions, but also at least I can to some extent tell what I’m looking for (side note: I don’t know the category in d. is the same as that in c.; I’m a compatibilist and take no stance on determinism, but if determinism is true, then there are no multiple branches in the category in c., but there are in the category in d.); this might be causal possibility in a world like ours, but without fixing the past.
e. If I’m considering what’s nomologically possible, I would have difficulty since I’m not sure how the world is meant to be divided between ‘nature’ and ‘non-nature’.
As I mentioned before, I think that the category “metaphysically possible” is the one mentioned in b. But if someone says that that’s not the case, I would be inclined to ask them what they mean by “metaphysically possible”.
Granted, usually it’s maintained that this is a primitive notion, used colloquially as well, etc.; that may be so if “metaphysically possible” is the category in b., but if it’s not, then I don’t see good evidence that I have such notion (unless the category is one of the others listed above); intuitively, I would use the word ‘impossible’ differently depending on what kind of impossibility I’m talking about, but I have to have some idea of what impossibility I’m talking about in mind.
On the issue of what blocks scenarios involving temporal density, my question was what blocks them in cases in which the existence of the entities in question is possible. If I understand your position correctly (please let me know if I don’t), you’ve not ruled out the possibility of infinitely many reapers, angels, etc., in a finite past.
So, my question would be like the following one:
Assuming it’s possible that there are infinitely many unembodied beings {U(n)} in a finite past, what would prevent U(n) to decide in 2014 (or be programmed to or ordered to, etc.) to assert between t0+1/(n+1) seconds and t0+1/n seconds “I like the number n” (where t0 is sometime in, say, 2015), and then carry out their decision?
If causal explanations that vary from scenario to scenario are ruled out, I’m not sure how that would be blocked.If an answer is that what would make that impossible is that temporal density is impossible, then why can’t the same answer be used in response to the GR argument against things coming into existence uncaused, or against infinitely many past events one before the next in infinitely many past years? (infinitely many past years but with no infinite chains of events one before the next between two given times or between two given events).
On the issue of certain causally and spatially disjoint things that can coexist, I would expect that one of them could be destroyed without destroying the others…in some scenarios involving those things, but not in all (note: please correct me if I’m not tracking you here, but it seems to me you’re not using ‘could’ in the sense of power, but in the sense of metaphysical possibility; I don’t think they’re the same).
For instance, in some scenarios like that, it would be impossible to destroy any of those things, and thus it would be impossible to destroy any of them without destroying the others.
A scenarios like that would be as follows:
S1: There is a being B who rules the world effortlessly (there is no stipulation of necessary existence), and such that it’s psychologically impossible for B to lie or break a promise, due to its mental makeup. It’s also causally impossible for something to happen against the will of said being. That being creates two beings B1 and B2, promising each of Bj that she (i.e., B) will ensure that Bj will last forever (in Heaven, Hell, something else, or without specifying; that’s not required).
Then, it seems it’s not possible for B1 or B2 to be destroyed, and thus to destroy one of them without destroying the other is also impossible.
In terms of metaphysical possibility, there is no metaphysically possible for a scenario S1′ that is like S1, and then has an added condition that B1 (for instance) is destroyed.
Regarding jointly exercise of their powers, it might or might not be possible for them to jointly exercise them. As you say, maybe something blocks them. But there might be scenarios (as far as I can tell) in which it’s not possible for them to exercise their powers together, even if nothing prevents them from doing so.
In fact, as far as I know it would even be impossible (if determinism is possible, which seems very plausible to me, but you probably don’t agree, so that would explain a disagreement on the matter) for one of them to exercise its powers.
For instance, consider a deterministic scenario S2 in which there is a bomb B3 with the power to explode and destroy a rock. But we also include deterministic conditions in S2 that entail that B3 will never explode. Then, there is no possible scenario S2′ with the same conditions as S2 in which B3 exercises its power and explodes. One may also construct scenarios in which it’s not possible for some beings to jointly exercise their powers, etc.
Of course, the introduction of God in every possible scenario would make the bomb scenario impossible, so I wouldn’t expect you to share that conclusion, but to answer your “wouldn’t you?” question, my answer would be “It would depend on the specific conditions of the scenario”.
I would need more time to think about the question under the assumption that God exists necessarily.

The sticking point for me is that *if* certain causally and spatially disjoint things *can* co-exist exist, then I’d expect that any one of those things *could* be destroyed without thereby destroying the others (wouldn’t you?); and if things have certain disjoint powers, then I’d expect it to be *possible* for those things to jointly exercise their powers–except in situations where they are blocked by something (or each other).

Let’s assume that that is true, and let Asserter#n be an entity that has the power to assert (at least to herself), “I like the number n”, between t0+(1+n+1 seconds) and t0+(1/n seconds), but they don’t have the power to block others from asserting stuff.
Then, it seems to me that it’s possible for any finite number of them to exist and exercise their powers together (assuming that time is not rigidly discrete).
However, and going by the assumption, it also seems to me that one of the following statements is true.
1. It’s impossible for all of them to coexist.
2. It’s possible for all of them to coexist, but impossible for them to jointly exercise their powers, and therefore in every possible scenario in which they coexist, something blocks them.
3. Possibly, time is dense.
If 3. is true, GR arguments (in general) fail.
If 2. is true, then there must be a causal structure that blocks Asserter#n for infinitely many n, at least in any scenario on which they all coexist; but then, the same reply may be given in the case of the GR scenarios.
If 1. is true, then one might ask why it’s not possible for them to coexist.
i. If the answer is that it’s impossible for them to coexist because time isn’t possibly dense and their powers would entail it, then it seems to me that the same answer would block a GR argument argument against a beginningless infinite past, and a GR argument against objects coming into existence without a cause.
ii. If the answer is that actual infinities are impossible, then I would be inclined to ask why that is so. But in any case, if that is the answer, it would also seem to block GR arguments.
Then, whether an infinite past would be possible would depend on whether that would count as an actual infinity (on presentism, it seems to me it does not, ironically given that the KCA is usually defended on presentism; still, I don’t think presentism is true, anyway, so plausibly that would entail no infinite past), and whether things possibly come into existence without a cause would require further analysis, but the GR argument would be blocked.
iii. If the answer as to why 1. is true (assuming it is) is something else, I would be inclined to ask what that answer might be, and why it would not work against GR arguments too.

Dianelos,
After further consideration, I still don’t see a way out for what I see as some of the problems for an interpretation that includes both an ontological interpretation of collapse and a requirement of consciousness for collapse to happen, plus rules out conscious states superposed with other states.
However, now I think I’ve not stated some of the problems clearly enough, and also a part of my explanation of the decay problem is not correct (by the way, the objection based on evolution, geology, Big Bang cosmology, etc., is a usual objections, not objections I came up with).
So, I’ll try to explain the difficulties I see more carefully, and give a couple of new arguments as well.
1. The last non-conscious state (the last so far, at least) of the universe would be at some time t0. Up to that point, everything is a big superposition state. The next time would be t0+e, and there is some conscious brain at t0+e, and there is no big superposition state at t0+e. So, it seems that change from the big superposition state to a state without the big superposition is from t0 to t0+e. But consciousness does not exist until t0+e. So, it seems that the change from a superposed state to a non-superposed state was brought about by the superposed state itself, with no consciousness. But then, it seems that a transition from a superposed state to a non-superposed state does not require consciousness, and can be caused by the non-conscious superposed state itself. Given so, the requirement of conscious observers to collapse the wave function seems puzzling.
2. I don’t see a way around 1., but let’s say for the sake of the argument that there is one, and let’s say that the first conscious brain on Earth existed, say, 700 million years ago, to give it a number; the problem works with other numbers too.
That is not the first time at which some brain capable of consciousness might have existed, given earlier conditions, since a Boltzmann brain had a very low probability but still might have happened before 700 million years ago, given previous states of the world.
But that raises a question: why didn’t the big superposition collapsed whenever it contained a brain capable of consciousness, even before 5 billion years ago?
From a different perspective, if there were earlier superposed states involving brains complex enough for consciousness, but without consciousness, what then, caused one of them to become conscious later?
Being more probable than previous such brains does not seem to do the trick, since the superposed state contains all of the possibilities anyway, and both probable and improbable states do not come to obtain via earlier collapse, for some reason.
I see no way around this problem, either, but let’s assume for the sake of the argument that an answer exists. It remains the case that even though it did not actually happened, given it was still possible given previous states that such collapse involving a conscious Boltzmann brain would have happened, which results in the following problems (among others):
3. So, let’s say that the first conscious brain existed on Earth about 700 million years ago. Then:
a. Despite our measurements based on radioactive decay, it’s not the case that the Earth existed 4 billion years ago. Rather, 4 billion years ago there was a big superposition of states, some of which contained the Earth, and some of which did not.
If, say, a Boltzmann brain had become conscious 2 billion years ago (improbable, but possible), it might have collapse the wave function of the big superposed state in a way that would have resulted in the non-existence of the Earth, ever. So, even 2 billion years ago, an event might have happened that would have resulted in the Earth’s never coming into existence, which shows (barring, perhaps, time-backwards causation) that, on this interpretation, it is not the case that the Earth existed 4 billion years ago.
The conclusion, it seems is that the Earth only existed for 700 billion years. Our measurements based on radioactive decay (which also didn’t happen before consciousness; rather, there was a superposition of states in which some particles have decayed, and stated in which they had not) give false results, based on the assumption that decayed happened when it did not.
b. Similarly, the Sun did not exist 4 billion years ago, and stars, galaxies, etc., did not form when we think they did. The same goes for early formation of nuclei, etc.
Rather, there was a massive superposition up to 700 million years ago, when everything collapsed and made it look as if all those things had happened in those earlier times. But as before, if, say, a Boltzmann brain had become conscious 800 billion years ago, then perhaps the Solar System would never have existed, and neither would, say, Alpha Centauri, which means those things did not exist 800 million years ago.
c. For similar reasons, there was no evolution earlier than 700 million years ago. The first conscious brain in question didn’t actually evolved, but came into existence and made it look as if it evolved.
4. After consciousness, the problem in 3. would be even compounded if, say, it’s stated that the Moon does not exist when no one is watching.
It might be assumed that (like Alexander suggested) that there are entangled states being collapsed by measurements even if most of the entangled stuff is not directly observed.
However, there appears to be no good reason to believe so. Indeed, if all the early universe, evolution, etc., never existed before 700 million years ago, there might be plenty of other things that are just appearances resulting from other massive collapses, even if less massive.
5. Side note: it seems von Neumann’s postulate does not work given present-day evidence (e.g., see this Wikipedia article) for sources.

Angra, nice breakdown of options.
I have questions. Here is one. Why would the “no infinities” option block the GR argument? Wouldn’t the reasoning be “if the past could be infinite, then there could be an actual infinite, but if there could be an actual infinite, then, by assumption of the option, there could be situations that are modally contiguous with the GR scenario…”? (BTW: “ersatz” presentists would think there actually are past-tense times–to ground truths about the past.)

Angra,
1. I disagree with âQM is intended to describe the world around us at low levelâ. In fact QM only describes (and, significantly, mathematically models) physical phenomena. There are many worlds that would produce the same physical phenomena, as evidenced by the fact that people have come up with various ontological interpretations. Further QM is not really about âlow levelsâ, in the sense that there are no low level phenomena. Thus we don’t see an electron, but hear clicks, or see bubbles. It is the latter phenomena that QM describes. Indeed, the very fact that physical objects around us are visible in reflected light is a (quite complicated) quantum phenomenon. We live in a quantum phenomenal world.
Now, in classical science theories entail (or nearly entail) a mathematical model of reality which if real would produce the phenomena the theory describes. Scientific realism is the idea that such models are indeed real. Most physical scientists are scientific realists, simply because it is easier to think about models making a realist picture of them. (Actually, by the age of three we are all scientific realists, since we interpret the order present in our visual experience as referring to actual physical objects around us producing them.) But QM proved a very hard nut for scientific realists to crack. For one, QM describes all physical objects (whether an electron or the moon) existing as fields and thus in many places at once. Some scientific realists interpreted this literally (Copenhagen), but others interpreted this as meaning that the same object exists only in one place in our universe but also in other places in other parallel universes (many worlds). The fact that when we look around we always observe objects in one place (or in general having concrete physical properties) was also interpreted differently, Copenhagen saying that the objectâs field (or wavefunction or state vector) collapses when observed. And whatâs worse than mere disagreement, scientific realists found themselves describing remarkable features of reality that are nowhere to be found in the actual theory, such as observation-caused collapse of the wavefunction (Copenhagen), or the splitting of the universe in many copies (many worlds). I think it is fair to say that QM proves that scientific realism is far from evidently true.
In real life many practicing physicists found that they could work with the equations and even win Nobel prices in physics without making any mental picture of reality, or perhaps while inventing some mental picture of reality without caring whether itâs true or not, or indeed while jumping among different mental pictures of reality depending on the kind of work they do. Thus the failure of agreeing about the metaphysical implications of the theory, or indeed about how the world is at its most basic parameters (one universe or many?, fields or particles?, indeterministic or deterministic?), has not in any way slowed down the physical sciences, which once more evidences that the physical sciences are not about how the world is, but only about how (part of) the world seems.
Even though scientific realism is the dominant view among physicists, there are also non-physicalist ontological interpretations, such as the idealist interpretation. According to idealism quantum phenomena are produced by Godâs will, physical objects (whether an electron or the moon) exist as ideas in Godâs mind, and when we observe them God produces for us phenomena the statistical properties of which comport with the amplitudes of the wavefunction. I donât know of any physicist who is an idealist, but being an idealist is certainly no impediment â in fact in may be an advantage. My point here is that QM is a hard nut to crack only if you have made certain metaphysical assumptions.
Finally, since for hundreds of years physical scientists are overwhelmingly scientific realists and wrote about science as if scientific realism were true, the language one commonly uses when speaking about science tends not be neutral on this, or at least the common understanding of such language is the one entailed by scientific realism. Thus, even though I am an idealist myself, when I wrote that âQM is a complete theory of physical systemsâ I imagined physical systems the way scientific realists do. I should have written that QM is a complete theory of physical phenomena.
2. You are right to observe that we havenât yet discovered a theory of quantum gravity, but since it is almost certain that such a theory exists it does not affect my argument in a significant way.
3. My argument is about what I find to be the best understanding of a Copenhagen-like collapse-based scientific-realist interpretation of QM. How exactly the founders of the Copenhagen interpretation (Bohr and Heisenberg) thought is not my main concern. I know there has been quite some debate about whether âobservationâ should be understood as âconscious observationâ or as âphysical event which classically fixes the result of an experimentâ. Since it is virtually certain that quantum physics applies to the whole of physical reality (or to the whole set of physical phenomena) and that therefore there are no classical regions in reality, the latter understanding makes no sense, and thatâs why I embraced the former. Also, it is I think a matter of historical fact that many eminent physicists, who later embraced Copenhagen, thought that consciousness is of the very essence, as evidenced by the long string of quotes by them (which I linked to in the previous post). But, again, my concern is not whether I am justified to call the interpretation I here expound âCopenhagenâ or not, even though I think I am. But I might as well call my interpretation the âVolos interpretationâ, and avoid the issue.
So the claims I make about the Volos interpretation is first that it is a viable one, since it fits all the data – both with QM and with our observation of the world around us. Further it describes in detail the ontology of collapse based on a very small number of metaphysical principles (it prohibits conscious states to exist in superposition, it prohibits a conscious brain to exist in some state inconsistent with the state of the consciousness it expresses), it satisfies the intuitions behind the PSR, it comports with the common assumptions of the mind-body philosophy, and it even makes some testable predictions about the large scale properties of the observable (concrete) universe.
4/6. As you rightly surmise the Volos interpretation does not say that collapse is caused only by the conscious observation of physical objects, but by conscious experience itself. Even when we are lying on a soft mattress in a completely dark room thinking, say, about math â the fact that the experience of our thoughts is of a concrete nature entails that the wavefunction of our brain will collapse to the physical state that corresponds to these concrete thoughts. This feature of the Volos interpretation reflects the principle widely accepted in mind-body philosophy about there being a perfect correlation between conscious states and brain states (even though nothing as strong as supervienience is assumed â thus C(brain state X) may be identical to C(brain state Y) ).
As far as I can see the Volos interpretation (as any conscious-observation based Copenhagen interpretation) does not suffer from any problems related to measuring geological age, or to making sense of natural evolution. A physical object in a superposed state is not less ârealâ, only there is no conscious subject experiencing it. I know it reels the mind to think that what QM permits is actually real according to the realist interpretations of QM. Actually in the many worlds interpretations all that is permitted is concretely real albeit in a different universe, so there are universes out there where each one of us will never die, and others where the Statue of Liberty suddenly took to swimming around Manhattan, others where Richard Dawkins after publishing his God Delusions recanted and became the Pope, and others where life on Earth is dominated by intelligent reptiles. Scientific realists who become aware of such absurdities either respond by arguing that reality is stranger than we can imagine â or else reject many worlds. Or else bet against QM being true (see next point).
5. I thought Weinberg favored the many worlds interpretation, since he did once write that in his experience this is the interpretation embraced by most working physicists (who actually care about what QM says about the world). In the paper you link Weinberg does not propose a new ontological interpretation of QM, but rather a âcorrectionâ of QM itself â as he explicitly makes clear in the introduction. There have been other such attempts, for example the GRW theory, which also depends on spontenous wavefunction collapses. All such theories in order to get off the ground must describe phenomena in a way which is so close to QMâs that no easy experiment can be devised to test whether they or QM is true. But given QMâs momentous success, and given that these alternative theories are ad-hoc constructions designed to allay their authors subjective distaste for QMâs metaphysical implications (as Weinberg writes he personally finds none of the interpretations of QM to be âentirely satisfactoryâ), there is little warrant for them being true. Unless one should think that subjective metaphysical preferences justify oneâs belief in different scientific theories.
6. I am not saying that the kind of move Weinberg makes is unreasonable. Oneâs worldview (or noetic structure, as some might put it) consists of a network-like set of related beliefs, and when faced with disturbing evidence which does not seem to fit, a common energy-saving epistemic response is to try to shift the network without changing its character in order to make place for the new evidence, rather than tear the whole thing down and replace it with something entirely new around the new evidence. In our case, since the worldviews of scientific realists tend to be materialistic, the very fact that a particular ontological interpretation of QM entails that consciousness is primary is reason for such scientific realists to reject it in favor of some other interpretation. For even though the other interpretation may entail some significant shift in their worldview (e.g. a shift away from the belief that each one of us only exists in this universe), at least it does not tear down the materialistic character of it.
Further, you write: âunder the interpretation you described, it still seems to me that the change from a superposed state at t=e to a non-superposed state at t=2e was not caused by consciousness (which didn’t exist until t=2e). â
Right â thatâs why I presented the less granular timeline afterwards: At t=2e the brain is moved by the deterministic evolution of the wavefunction into a superposition of many physical states, one of which (the s211) is consciousness-expressing. At t=3e that consciousness is expressed and C(s211) obtains. But its coexistence with a brain in a superposed state is metaphysically prohibited (in the appropriate sense of causing the necessary change to remove the prohibited state of affairs). Which causes the collapse of the brainâs wavefunction at t=4e where the brain exists in just one physical state B(s211). But again: My killer argument is that the ontological process described can be simulated in a computer program, which proves that it follows well-defined causal rules.
You point out some weird implications of the Volos interpretation, such as that life forms which have evolved within physical states of the universe present in the massive superposition of the universeâs wavefunction would disappear from concrete reality once the very first conscious brain and its respective conscious state becomes actual. True. But the same holds on all versions of ontological Copenhagen, for on all such versions the collapse entails that possible physical states will for ever stop existing as potentially observable (concrete) reality. Once you open the box and find Schroedingerâs cat dead, nobody will ever observe that cat growing old â even though that cat growing old does exist within the massive superposition of the universeâs wavefunction.
You suggest a potential problem for the Volos interpretation (and indeed for all âconscious observation causes collapseâ interpretations), which obtains if within the massive superposition the first conscious X evolves at time tx on planet P, and the second conscious Y evolves at time ty on far away planet Q, with tx close to ty. I have to think about that and will comment in a future post.
About how to compute t1(insect brain): Find a supercomputer, feed it the physical laws and initial conditions of our universe, and have it compute the entire deterministic wavefunction of the universe, i.e. the massive superposition of all state histories. Then check to see when at the earliest an information processing system of the complexity of an insectâs brain in some state history evolves. This earliest time is t1. All of that is of course theoretical, in the sense of not being feasible using any conceivable future technology. But on the other hand it suggests that under some metaphysical assumptions it is not logically impossible to use physical science to ascertain whether a brain is capable of consciousness or not. It gives one a glimmer of hope that physical sciences might after all be of some help for solving the hard problem of consciousness. And should such an experiment turn out to be feasible and we did find a t1=t2 then it would also confirm the metaphysical assumptions on which it rests, for it would prove that the observable world is optimized for the evolution of consciousness.
Finally, about my nomenclature: âPhysicalâ Iâd say characterizes all concepts used in the so-called physical sciences which might be interpreted as referring to actual existents. Thus we all agree that it is reasonable to speak of physical apples, stars, genes, forces, spacetime, energy, fields, quarks, strings. But usually we donât speak of physical numbers, physical addition, physical red, physical ideas, physical ethical value, physical conscious experience â even though some physicalists think we should. Actually there are two classes of non-physical concept. The concepts that do appear in the physical sciences such as numbers or addition, but are not considered to refer to actual existents. And the concepts that do not appear at all, such as red, conscious experience, ethical value, beauty, God â the existence of which is therefore is a useless hypothesis in the physical sciences.
âMetaphysical naturalismâ refers to the idea that all the properties of whatever exists (whether physical or not) evolves by blindly following mechanistic laws, i.e. laws fully described by math (whether deterministic or probabilistic, whether analytic or algorithmic). To put it uncharitably, naturalists imagine that the world is not more interesting than what can be captured by mathematical formulae.
(I did not read your last post before starting writing this one. You again raise some problems Iâd like some time to think about.)

Joshua,
Regarding your question, I would say that ‘no infinity’ blocks the GR argument because the argument requires infinitely many reapers.
So, if the ‘actual infinities are impossible’ reply blocks the argument for temporal density by means of denying the possibility of infinitely many reapers, then the same reply seems to block the GR argument as far as I can tell.
On the other hand, the ‘no infinity’ reply can be used, on its own, against an infinite past, except for the presentism reply (no “ersatz”; what I had in mind was presentism combined with a tensed theory of time; thanks for pointing out that alternative).

Wouldn’t the reasoning be “if the past could be infinite, then there could be an actual infinite, but if there could be an actual infinite, then, by assumption of the option, there could be situations that are modally contiguous with the GR scenario…”?

I think that the GR aren’t needed there, since on the assumption that actual infinities are impossible, it would be enough to say something like ‘if an infinite past could be infinite, there could be an actual infinite, but that’s not possible’.
However, a potential reply to that argument (or one using GR) would be ‘if the past could be infinite, since there are no possible actual infinites, then a presentist tensed theory would be true’, or something like that.
In any case, the issue would only revolve around the question of whether an infinite past would entail an actual infinity, not whether GR scenarios are possible.
Aside from the GR argument against an infinite past, the ‘no infinity is possible’ argument would block the GR argument against things coming into existence without a cause.
In that case, a reply to “if things could come into existence without a cause, then a contradictory GR scenario would be possible” would be “No, because actual infinities are impossible, so only finitely many things could come into existence without a cause”.
Granted, someone might leave aside the reapers and try something like ‘if things could come into existence uncaused, then infinitely many things could do so, but that’s impossible”.
That, however, is a different argument, not a GR one (personally, I get the intuitive impression that this line of examples should stress that this type of modal argumentation isn’t good, but I’m keeping the assumptions for the sake of the argument, etc.).
Side note: in any case, all of this has the cost of a commitment to the impossibility of actual infinities, which I think would have far reaching consequences, beyond GR scenarios and similar issues.

(I did not read your last post before starting writing this one. You again raise some problems Iâd like some time to think about.)

Okay, so I will address some other issues in your reply and leave the problems in question for later.
1. On the issue of only describing ‘physical phenomena’, I don’t think that QM is meant to divide the world around us between ‘physical’ and ‘non-physical’. It’s meant to describe everything around us the best they can with the tools available. The interpretations are also part of the attempt at such description, and they do disagree significantly. They’re trying to figure out the right one. Even to this day, a number of physicist are trying to come up with testable predictions to tell them apart.
By ‘low level’ I meant to imply that it describes things in terms of electrons, quarks, etc., while (say) a human intuitive description would use concepts like chair, water or cat. It’s not that QM does not describe the stuff that we see, but that it describes it in terms of the things I mentioned above.
What’s ‘low’ of course is relative to context. One might think of a potential future description at the level of some stuff that makes up the particles QM deals with.
That said, it seems the ‘low level’ issue may be left aside if you disagree, since I would also say that QM is meant to describe the world around us (without specifying ‘low level’), without trying to make a distinction between things that are described (‘physical’) and things that aren’t (yes, granted, you may well disagree with that too).
On the issue of whether not having a picture of reality has slowed down the physical sciences, I would say that precisely that’s a slowing down on its own, in the sense that phycisists are still trying to figure out what’s there, new models are proposed, etc. and they haven’t been able to come up with a picture that is satisfactory so far.
I don’t agree that physical sciences are not about how the world is (at least for many, probably most theoretical phycisists) – and I would not agree that they should not be about it, though I don’t know whether that is your view.
In particular, scientists work on issues like the size and age of the universe, how many planets are out there, how black holes form, what the future of the universe will be, etc., which are clearly (for most) matters of how the world is, and their disagreement is also about how the world is (or was, will be, etc)).
Also, I would not consider the ‘idealist’ approach not a view of how the world is (even if it’s a world with a mind making it look in a different way), though I don’t think that the idealism you mention (i.e., including God in the theory) should be consider on par with the other interpretations, for a number of reasons I’d rather leave for another time if that’s okay with you, since debating the truth and/or warrant for theism (which we might have to if we continued on this road) would take way too long for me or for this thread.
2. I made that point in reply to the claim that QM is assumed to be a complete theory of physical systems.
3. I would say that the debate is not only about conscious observations vs. classical regions. There are physicists who reject both – and I think there are excellent reasons for that -, even on an ontological understanding of collapse.
Regarding your assessment of the viability of the Volos interpretation, I don’t agree for the reasons I’ve been explaining, though I can see that you don’t find some of them persuasive. But as I mentioned, I’ll wait until you consider the points I made in my other post before going any further.
5. Yes, he’s suggesting a correction, though he’s still thinking about wave functions and collapse, and I think that the kind of corrections in question may well be what he’s talking about when he speaks of progress (or maybe more precisely that the proposed corrections are based on some progress made before).
I don’t agree with your negative assessment about those theories, though; rather, I think that they’re attempts to describe the world better. You may call it ‘subjective dislike’, but for that matter, one may call it ‘subjective dislike’ when people reject Many Worlds and embrace some other interpretation, etc.
Moreover, if another theory makes predictions similar to those of QM and supports an intuitively more plausible ontological view (e.g., not rejecting other sciences, like geology, biology, etc.), I don’t think that it would be proper to dismiss it or even consider it less plausible just because QM was proposed first. (what if it had been the other way around and the other one had come first?) I would rather wait until experiment can tell them apart, and take no stance for now, unless I have independent reasons for doing so.
6.
You write:

Right â thatâs why I presented the less granular timeline afterwards: At t=2e the brain is moved by the deterministic evolution of the wavefunction into a superposition of many physical states, one of which (the s211) is consciousness-expressing. At t=3e that consciousness is expressed and C(s211) obtains. But its coexistence with a brain in a superposed state is metaphysically prohibited (in the appropriate sense of causing the necessary change to remove the prohibited state of affairs). Which causes the collapse of the brainâs wavefunction at t=4e where the brain exists in just one physical state B(s211).

My objection was based on the first timeline you offered. Regarding the second (i.e., the less granular) timeline, I would say that at t=3e, the brain exists in a superposition of states, one of which is conscious, and the other is not. In other words, at t=3e there is still the big superposition, and yet there is consciosuness. I thought that you were trying to rule that out. If you didn’t, then that is not a problem.

But again: My killer argument is that the ontological process described can be simulated in a computer program, which proves that it follows well-defined causal rules.

Okay, but that’s not the concern I was trying to raise. The process may well follow well-defined causal rules that contradict some assumption (e.g., entail that collapse is not caused by consciousness, which is the problem I was raising, though on the second, less granular view, the reply would be different (see above)).
On the issue of ‘physical’, thanks for the explanation.
I mentioned the world around us, and I don’t think that numbers, propositions, etc., count (I wasn’t talking about that, anyway; I don’t think physics intends to describe that, of course).
Regarding conscious experience, while physics does not talk about it, I don’t think it’s meant to leave it aside in the sense of not trying to come up with models that apply even to conscious entities the best we can (i.e., if it turned out that QM does not hold in a working brain, scientists in the future would almost certainly look for a theory that did). If it turned out that that’s not doable (at least, not for all conscious entities), that’s another matter, but that too would be a significant breakthrough in my view (but I’m not suggesting that that will happen).
On the issue of what you call ‘ethical value’, I think agents value things. More precisely, my position is that ‘value’ is a verb; a nominalization would be okay for the purposes of talking conveniently, but in my view a commitment to some ontological claim of an entity ‘value’ would not be correct (I’m not denying objective moral statements and truth, by the way; I think that’s another matter, though that’s also probably a matter for another time), and science (including physics) intends to be able to describe agents as well, even if on a different level (i.e., in terms of particles and stuff, not in terms of what they value, feel, etc. – not for the most part, at least).
But as above, a discussion (defense of those positions, critique of opposite views, etc.) would make the posts in our exchange unmanageably long and would take too long as well (at least for me), so I’d rather leave it at that if you don’t mind.

Thanks Angra.Regarding your question, I would say that ‘no infinity’ blocks the GR argument because the argument requires infinitely many reapers.
Here is how I’m seeing it. First, no premise in any GR argument implies that there can be infinitely many reapers. GRAIP implies that *if* there can be infinitely many past events, then there can be infinitely many reapers. I took it that the ‘no infinity’ option was one explanation of why a certain GR-like scenario would be impossible (where its impossibility might be obtained given certain recombination premises).
The idea here is that given certain recombination premises, if the GR scenario is impossible, then certain neighbors are too, in which case one may ask where the modal boundaries lie. One answer is the divide between infinite and finite–which implies no infinite past (given certain views of time). (There are other answers.)
(BTW: ersatz presentism is usually taken to be a tensed theory.)

Thanks Joshua,
I’m not sure I’m tracking you properly. The ‘no infinity’ option was assumed to be an explanation of why it’s impossible for Asserter#n to coexist, for all n. Applied to the GR, it would be used against claims that if certain things obtain, then a contradictory GR argument would obtain. For instance, let’s consider GRAUB.
The argument is:

Suppose uncaused beginnings are possible. Then it would seem to be possible for there to have been any combination of events (beginnings) that occur without a cause. Why should size or shape or degree of causal capacity of things that begin to exist make a modal difference here? It seems they wouldn’t. Thus, it would seem to be possible for any number and any combination of GRs to come into existence uncaused. But then it follows that it would be possible for a grim reaper scenario to obtain without a cause. Thus, since a grim reaper scenario is impossible, so are uncaused beginnings.

I was thinking of a reply like:
“But even if uncaused beginnings are possible, infinitely many entities (concrete particulars) coexisting is not, so the GR scenario could not happen.”
But as I mentioned, someone might say: “if things coming into existence without a cause are possible, then infinitely many things possibly come to exist, which is impossible. Hence, there are no possible uncaused beginnings.”, but the other side might insist “Infinitely many things are impossible, hence infinitely many things coming into existence without a cause are impossible, even if it’s possible that some things come into existence without a cause”.
Which one wins?
I do not take a stance on that (personally, I think actual infinities are possible, but I don’t find GR-type arguments persuasive for reasons mentioned earlier), but I think the argument does not revolve around GR. Also, I’m not sure what kind of GR ‘neighboring’ scenario might be construed using GRAUB. Do you have any specific candidates to neighbors in mind, or some specific recombination premises that would be applicable in the scenario involving things coming into existence without causes?
Regarding GRAIP, the reply would be something like: “Maybe there is an infinite past, but that’s not an actual infinity (on some views of time). Whether other reapers existed in the past, there are only finitely many at every time, and so no contradiction is entailed.”
Granted, on other views of time, an infinite past entails an actual infinity, so someone might say “If an infinite past were possible, that would be an actual infinity, but that’s impossible”. But the GR don’t seem to be playing any role.
Question, just to clarify: do you consider that ‘no infinities are possible’ is actually the proper reply in the case for temporal density using Asserter#n, for all n?
Briefly, an argument from actual infinities to temporal density mirroring (as I understand it) the type of reasoning used in GR arguments would be as follows:
P1: If actual infinities are possible, infinitely many asserters are possible.
P2: If infinitely many asserters are possible, then time is possibly dense.
P3: Actual infinities are possible.
C: Time is possibly dense.
On the other hand, someone might use a GR argument against temporal density to conclude that C is false, and then use that in conjunction with P1 and P2 to conclude that P3 is false.

Angra,
Let me start by describing the potential problem that bothered me. I wonât describe it in detail, since I donât intend to solve the problem, but rather demonstrate that it disappears when one looks closer at the ontology of the wavefunction collapse. Suffice to say that the problem is based on the following localized view of wavefunction collapse: The idea is that in order to maintain mind-body correlation, a concrete conscious experience âcollapsesâ all brain states that are not consistent with it. Now the brainâs physical state is entangled with its physical environment, and therefore all physical states in oneâs environment which are not logically consistent with the collapsed physical state of oneâs brain will also collapse. One ends up visualizing physical reality as being a haze of superposed physical states with bubbles of conrecte/observable states emanating at great speed around conscious brains. Brains existing at close proximity (as are ours here on Earth) maintain mutual consistency, and thus one visualizes a bubble of internally consistent concreteness quickly growing around the Earth into a cosmos of still superposed uncollapsed physical states. So hereâs the problem: Should it happen that conscious life evolves at approximately the same time on two far away planets then the two planetary bubbles of internally consistent collapsed states may coexist and grow towards each other. Each babble is internally logically consistent, but they might not be mutually consistent. For example the evolutionary history of life on the first planet might entail that a particular large comet hit that planet stirring its evolutionary landscape in productive ways. And the evolutionary history on the second planet might entail that the same large comet hit it instead. So the obvious question is: What happens when the two expanding babbles of concreteness meet? Does a second order collapse obtain? These are messy issues. First of all it is not clear how to ascertain that this problem is real. And if it is then any solution will be ad-hoc.
Instead of trying to solve the apparent problem, letâs start at the beginning: QM and the initial state of the universe deterministically fixes the universal wavefunction, which is a tree-like structure. Here the initial state of the universe will evolve into a superposition of N states, which at the next time increment will evolve into a superposition of N*M states, and so on into an ever growing number of branches of âstate historiesâ. The whole thing is vast (and will indeed include state histories where Boltzmann brains and indeed Boltzmann planets will spontaneously form â more about this in a later post).
According to the Volos interpretation this massive superposition of the physical states of the universe is real. Instead of considering local regions of the universe, letâs stick with the view of the whole universe. We visualize time as a horizontal line moving upwards across that fixed tree-like structure of the universeâs wavefunction. At some point in time (when the first conscious life naturally evolves somewhere â for now we forget about Boltzmann brains) this line encounters complex brains, the superposed physical states of which would express mutually contradictory conscious experiences. When this happens nature randomly (or rather probabilistically, since it takes into account the amplitudes or weighting factors of QMâs wavefunction) picks exactly *one* state of the universe where such brains exist, and tags all other states and their future branches as âunobservableâ. Only in this one universal state will complex brains express their individual state into conscious experiences. In all other âunobservableâ states of the universe complex brains will exist but will not express conscious experience. (In other words, the sufficient condition for conscious experience is an appropriately complex brain existing in a not âunobservableâ state within the massive superposition of the universeâs wavefunction.) Finally, the tagging of all the other states and their future branches as âunobservableâ is what Volos means by the âcollapse of the wavefunctionâ. Thatâs basically all.
Here are some important implications of the above simple metaphysics: At each point in time all actual conscious experience exists in exactly one state of the universe within the massive superposition. Further there is exactly one state history of the universe where actual conscious brains exist. Each conscious brain (each individual) only has one conscious experience. Even though universeâs wavefunction includes âabsurdâ physical states (such as the Statue of Liberty swimming around Manhattan) the probability of people actually observing such absurdities is zero for all practical purposes (or, in other words, the one conscious state history will almost certainly not pass through such rare absurd states). Radioactive decay, natural evolution on Earth and perhaps on other planets in the cosmos, and in general the whole of the common metaphysics of naturalism obtains. The observed state of the universe is internally logically consistent (and trivially so, since absolutely all states in the massive superposition are internally logically consistent). The list of phenomena that are used to describe âquantum weirdnessâ (the dual wave/particle nature of particles, delayed choice experiments, non-local phenomena, etc) are easily and naturally accounted for. In particular delayed choices in no way entail some kind of causal power over the past, since all state histories of the world are fixed, and this includes the one which has led to the state in which now conscious observations exist (i.e. the state which we observe when we look around).
Under the above clearer description of the Volos metaphysics letâs reconsider the problematic case described at the beginning of the post. Consider then conscious A and B in a room observing an experiment with two allowed results x and y, and conscious C and D observing another experiment in a different room and which may produce z and w results. Further letâs assume that Ax means âAâs brain experiences result xâ. Then all states of the universe in the massive superposition of the universeâs wavefunction will belong to one of the following four sets:
Ax Bx Cz Dz
Ax Bx Cw Dw
Ay By Cz Dz
Ay By Cw Dw
According to the Volos interpretation at this point in time nature will tag as âunobservableâ all states of the universe but one, in which the corresponding conscious experience will obtain. That one state will exist in some of these four sets. Letâs suppose that the one state picked exists in the Ax Bx Cw Dw set. This means that A and B will experience x, and C and D will experience w. We see then that no possibility of inconsistency exists, whether the two rooms are in the same building, or whether they are on two different planets.
I have thought some about these issues and there are some intricate details. For example, mental states change tenths of orders of magnitude slower than physical states, and that should be reflected in a detailed exposition of Volos. Further the requirement of only one state not being tagged âunobservedâ is overkill. One can visualize nature randomly picking exactly one universal mental state instead of exactly one universal physical state â and tagging âunobservableâ only all physical states which contradict that mental state. This variant allows for a richer future of conscious experience, since at each point in time conscious beings while having one concrete experience of life will exist in many different physical states â thus allowing for a more variable future which potentially will be experienced.

Dianelos,
Thanks for your explanation of the Volos interpretation. I still see some problems, such as the following:
1. It does not explain what it means to ‘tag’ all other states as ‘unobservable’. Clearly, it does not mean someone is doing the tagging in a literal sense, so it’s not literal. But what does it mean to ‘tag’ a state as unobservable?
2. Let’s say that t0+e is the first time at which there is consciousness. At t0+e, one of the states (say, S1.1) in the massive superposition state is that which contains that conscious brain (say, B1), whereas all of the other states in that superposition state do not.
However, there are plenty of other states, like S1.2., S1.3, that contain the same exact brain B1, but are different in, say, distant galaxies and the like. Many of those states are no less probable than S1.1 (e.g., those that have some distant particles in a slightly different position), and plausibly there are also similarly probable states with very different features at long distances (different stars, different comets hitting planets, etc.).
Other, similarly probable states do not contain B1, but a very similar brain B2, etc., and there might be similarly probable states without anything like B1, but some other B3 in distant galaxies. So, the probability of that specific consciousness-expressing state is extremely low, and further, there plausibly are similarly probable states.
But if that’s the case, then it seems once again that very improbable conscious states obtain, which raises the following issue:
Let’s say that t0 is about 700 million years ago. Then, it was still possible 800 million years ago that some other (also improbable) state would have obtained instead â one that did not contain B1, nor many of the entities that allegedly led to the evolution of B1 before 800 million years ago.
So, it seems that it’s not the case that B1 evolved from those entities, since it was still possible based on the situation 800 million years ago that those entities would never have existed.
In fact, it seems that plausibly, the same could be said about the Earth itself. It was still possible 800 million years ago that the Earth could never have existed in the first place, so it seems the Earth did not exist 1 billion years ago â and the same goes for the history of early evolution of life.
Now, at this point, a supporter of the Volos interpretation might say that there is no difficulty: the Earth existed as part of the superposition, 800 million years ago; it’s just that states without Earth at 800 million years ago had not been tagged as ‘unobservable’ yet.
But that does not seem to work, for the following reasons:
a. There is the problem of what’s meant by ‘tagging’ as unobservable.
b. When we say that, for instance, there was no gas giant planet in the Goldilocks zone of our Solar System at any point from, say, 3 billion years ago to now, but the Earth existed, life was evolving, etc., we meant to make an ontological difference about the status of the gas giant in question and Earth at that time.
On the Volos interpretation, perhaps 2 billion years ago, the ontological status of Earth and the gas giant in question was the same: they were both part of the big unconscious superposition, and their probability was roughly the same (say, there is a brain B2 that had similar probability to B1 700 million years ago, and which could have collapsed the wave function with similar probability elsewhere in the universe). Even if that’s not the case (i.e., no alternative history without Earth with more or less similar probability at that particular point in time), even improbable states seem to be a problem. We don’t mean that 2 billion years ago, the Earth was more likely to later be tagged as ‘observable’ than the other planet. We meant that the Earth existed then.
So, our statements about the early universe would not be true.
But even assuming no alternative history without Earth with more or less similar probability at that particular point in time (but why? that does not seem to be explained), and even leaving aside for the sake of the argument less probable histories, there remains the case that alternatives to B1 and its evolutionary history of Earth were similarly probable as the history that leads to B1.
But when we say that (for instance) X is an ancestor of B1 that lived 1 billion year ago, but there were no organisms like Y 1 billion years ago, we meant to make an ontological difference about the situation 1 billion year ago.
Yet, 1 billion years ago, Y and X were both part of the superposed state, and their probabilities weren’t so different. Moreover, either one of them might have been tagged as ‘observable’ or ‘unobservable’ later. So, the claim that X is an ancestor of B1 that lived 1 billion year ago, but there were no organisms like Y 1 billion years ago seems to be false.
At this point, someone might suggest modifying what we mean by those claims, but that does not seem to work, either, for the reasons explained in 3.
3. On Volos, what makes the difference between states at which, say, states at which B1 (allegedly) evolves and states at which B2 allegedly evolves instead is not something that happened during the evolutionary history leading to the existence of B1, but rather, it’s something that happened only when B1 became conscious, or perhaps rather immediately before that.
So, it’s not the case that B1 evolved rather than B2 because of such-and-such fact in the past (relative to 700 million years ago) that caused evolution to go the way of B1 rather than the way of B2, but rather, 700 million years ago B1 became conscious instead of B2 (for no reason, it seems, since despite similar probabilities, nature ‘tagged’ the history leading to B2 as unobservable, picking the history leading to B1 instead), and that didn’t have to do with their respective superposed evolutionary histories.
So, it seems evolution fails as an explanation. It’s not that B1 evolved for such-and-such things that happened in the past relative to B1’s existence, or that B2 didn’t evolve for similar such facts, but rather, both histories existed without being tagged as ‘unobservable’ up to 700 million years ago, and only an event that happened 700 million years ago tagged the other (just as real) history as ‘not observable’, without anything in the histories themselves that made the difference.
For similar reasons, explanations of formations of planets, stars, etc., seem to fail as well.
So, it seems to me that, even if one modifies what we mean by ‘the Earth existed’, ‘such organisms existed/evolved, etc.’, Volos still results in the rejection of evolution (perhaps, for most of the history of Earth), geology (ditto), and astronomy of the early universe. All of those things (early stars, etc.) did not cause planets, etc., to go the way we see them, but rather, much later events tagged the alternatives as ‘not observable’ (whatever that ‘tagging’ means), and facts from the early universe, early Earth, and perhaps most of the time Earth existed, do not explain what happened later.
4. On a different note, Volos does not seem to predict that there will take a lot of time for the second conscious brain to evolve on another planet after the first conscious brain, since the tagging of all histories but one as ‘observable’ would not indicate that the history compatible with B1 does not also contain many brains close to being complex enough for consciousness on many other planets in the galaxy, many more on other galaxies, etc., at the time of the tagging. Those histories about what happens on other planets need not contradict what happens on Earth on the ‘tagged’ history.
For that matter, consciousness wouldn’t need to arise on Earth first. It might arise somewhere else, and then a number of other times on some (many) other places.

Any ontological interpretation of QM must add something to it, since by itself QM says nothing about the fact that we observe a concrete universe around us. It doesnât even say anything about consciousness. (One might argue that QM doesnât say anything about human biology either, but thatâs false. Given the theory of QM and the initial state of the universe human organisms are there somewhere in the universeâs wavefunction.)
What Volos adds is this: It states that there is a binary property of each physical state of the universe and that there is a blind (and hence naturalism-friendly, albeit indeterministic) mechanism which sets the value of that property to âobservableâ or âunobservableâ. And it adds that the sufficient condition for actual conscious experience is the presence of complex brain in an âobservableâ state of the universe. All of this is meant quite literally.
My purpose here is to find out which the most reasonable interpretation of QM is from the point of view of a scientific realist. I am not claiming it does not entail some feature one might dislike, only that there is much more to dislike in other interpretations. Now please observe that until the very first conscious brain nothing indeterministic happens. Natural evolution deterministically explains all physical events up to the appearance of the first conscious brain. After the introduction of consciousness into some state of the universe all other states and their future branches are tagged unobservable. Only that conscious state and its potential future states can hold consciousness. Now there will be evolutionary histories which happen to fall within the unobservable regions of the massive superposition. The state histories in these regions are still real, natural evolution works there, complex brains B2 and later civilizations will evolve there, but according to Volos they will be zombie ones, since no conscious being will ever be experiencing them. Letâs not forget that the universeâs wavefunction includes all physical states not prohibited by QM, and thus includes all physically possible life forms and all possible civilizations. But on Volos consciousness only exists in one state history of the universe, namely in that state within the massive superposition we are continuously observing around us. Now the idea of so many life forms and civilizations being unexperienced sounds sad, on the other hand Volos avoids the many far worse absurdities of the many-minds and many-worlds interpretations.
On the other hand, Volos does not prohibit the existence of conscious beings evolving independently from us. Here is how:
Suppose (with no loss of generality) that the first conscious brain evolved on Earth at time tc (about 700m years ago). There is a state history deterministically connecting the initial state of the universe with that first state at tc, which passes through the formation of our galaxy, the formation of our solar system with no gas giant in the Goldilocks zone, and finally the formation of the Earth with its geology and climate and with life evolving on it up to the point of the first complex brain. That state history from the beginning of the universe up to tc is fixed and entailed by QM. (Thus all of scienceâs claims about the early universe remain true. The only thing that changes is that on Volos that state history is the optimal one for the evolution of a complex brain â a claim that does not contradict any scientific knowledge we now possess, and which claim may one day be scientifically testable thus confirming or disconfirming the Volos interpretation of QM.)
Since tc the state history of the conscious universe grows indeterministically up to the current time, contingently actualizing ancient Greek culture, Beethovenâs Ninth, and the first presidency of Obama. But the state history of the conscious universe is not only about earthly life. Unbeknownst to us perhaps there is a planet âBetaâ in the Andromeda galaxy where natural evolution is also producing complex life forms, and only yesterday the first complex brain obtained there. Since yesterday then, when nature blindly picks only one state of the universe for âobservableâ status, that state will also include one physical state of that brain on Beta. Thus that brain on Beta will experience its own planet environment behaving in a generally orderly but ultimately indeterministic fashion – the same way we do. (As I have argued in a previous post I happen to think that the above state of affairs is unlikely and that in the conscious state history of the universe the second conscious brain will probably obtain much later than the first. But nothing particularly momentous for the viability or plausibility of the Volos interpretation turns on this claim, so I will leave it alone for now.)
A final point. When discussing in the context of QMâs wavefunction of the universe there are no such thing as âprobabilitiesâ. At each point of time there is a large number of physical states (each with its own past state history) possessing a particular property called amplitude or âweightâ. But all these states of the universe exist in the massive superposition. All possible life forms and all possible civilizations are there. Since they all exist none is more âprobableâ than the other. Once consciousness evolves natureâs mechanism which blindly tags one state as âobservableâ and all others as âunobservableâ takes into account the respective individual weights in a way that gives meaning to talk about probabilities. Thus we conscious humans can safely predict that we shall not experience the Statue of Liberty swimming around Manhattan. (Using QM one can actually estimate the infinitesimal probability that we shall experience such an absurd phenomenon.) Probabilities then only make sense when talking about the state path of the conscious universe.

Dianelos,
Rejecting an ontological view because one deems it extremely improbable is not the same as doing so because one dislikes it. To put an extreme example, someone might claim that the universe existed for 5 minutes but was made to look as it does, and such claim can’t be refuted empirically. It’s just that it’s too improbable to be taken seriously (i.e., one should assign it a prior so low that for all intents and purposes it’s zero, and nothing raises the probability from there).
Volos doesn’t only contain features one may dislike, but contains features that lead me to reject it as too improbable. As for the best interpretation, I don’t know.
I would say that collapse without consciousness is a possibility, even if it requires minor corrections; if that is ruled out, then I would say that all present-day interpretations of QM have their own problems, but the problems of the Volos are decisive. I’m not sure how decisive the problems of all of the others are (some also have decisive problems), so I take no stance.
Regarding your inclusion on Volos of a realistic interpretation of all other evolutionary histories (i.e., not ‘tagged’ as ‘unobservable’), and indeed all other physical possibilities, then that essentially makes Volos a zombie version of the Many Worlds Interpretation:
Indeed, all of the other histories, with all of those different planets, stars, galaxies, brains, etc., with things from Boltzmann brains to entire worlds full of humans, etc., are also real, but just don’t have consciousness.
Whether one calls those histories ‘many worlds’, ‘other worlds’, ‘parallel universes’, or ‘different states in the superposition that are tagged as unobservable’, in all cases they’re given an ontological interpretation.
Further, you say:

The only thing that changes is that on Volos that state history is the optimal one for the evolution of a complex brain â a claim that does not contradict any scientific knowledge we now possess, and which claim may one day be scientifically testable thus confirming or disconfirming the Volos interpretation of QM.)

Other histories seem to be compatible with the existence of the first complex brain at that time (e.g., histories that differ on what happens in distant planets, galaxies, etc.; there are plenty of those.
Moreover, it might even be that other brains have evolved at the same time.

(As I have argued in a previous post I happen to think that the above state of affairs is unlikely and that in the conscious state history of the universe the second conscious brain will probably obtain much later than the first. But nothing particularly momentous for the viability or plausibility of the Volos interpretation turns on this claim, so I will leave it alone for now.)

For the reasons I’ve given earlier, I don’t think that that conclusion is warranted. But I agree that nothing important to the plausibility of the Volos interpretation does rests upon that point, at least given our evidence so far.

A final point. When discussing in the context of QMâs wavefunction of the universe there are no such thing as âprobabilitiesâ. At each point of time there is a large number of physical states (each with its own past state history) possessing a particular property called amplitude or âweightâ. But all these states of the universe exist in the massive superposition. All possible life forms and all possible civilizations are there. Since they all exist none is more âprobableâ than the other. Once consciousness evolves natureâs mechanism which blindly tags one state as âobservableâ and all others as âunobservableâ takes into account the respective individual weights in a way that gives meaning to talk about probabilities. Thus we conscious humans can safely predict that we shall not experience the Statue of Liberty swimming around Manhattan. (Using QM one can actually estimate the infinitesimal probability that we shall experience such an absurd phenomenon.) Probabilities then only make sense when talking about the state path of the conscious universe.

Okay, so let’s say that B1 is the first evolved brain that becomes conscious at t0. Before t0, there is no such thing as ‘probabilities’.
However, before t0, say at t0-e for some very small e, there was another brain B1′ in the superposition, just like B1, but in a path of the superposition that is just slightly different. B1′ came from a path almost identical as B1, but just with some particles in slightly different positions at some earlier times.
Yet, B1′ does not become conscious, but B1 does. Why?
It’s not that B1′ was somehow improbable. There was no such thing as probabilities at t0-e. How does ‘nature’ choose that B1′ will not become conscious at t0-e?
You said earlier that:

According to the Volos interpretation this massive superposition of the physical states of the universe is real. Instead of considering local regions of the universe, letâs stick with the view of the whole universe. We visualize time as a horizontal line moving upwards across that fixed tree-like structure of the universeâs wavefunction. At some point in time (when the first conscious life naturally evolves somewhere â for now we forget about Boltzmann brains) this line encounters complex brains, the superposed physical states of which would express mutually contradictory conscious experiences.Â Â When this happens nature randomly (or rather probabilistically, since it takes into account the amplitudes or weighting factors of QMâs wavefunction) picks exactly *one* state of the universe where such brains exist, and tags all other states and their future branches as âunobservableâ.

Yet, nature cannot probabilistically choose at t0-e that B1′ does not become conscious, since there is no such thing as probability. But if B1′ does not become conscious at t0-e, why does B1 become conscious at t0?
Moreover, the matter of Boltzmann brains remains a difficulty, since much earlier than t0-e, say at t1, a Boltzmann brain BB1 existed in the superposition. That brain was fully developed. But it was not conscious. Given that there is no such thing as probability before t0, it makes no sense to say that a t1

Just to clarify, I was taking the “no infinity” option as being one candidate account of why certain neighbors of a GR scenario may be impossible. The role of the GR argument, then, would be to motivate the no infinity option. Once motivated, one then infers that, for instance, an infinite past is impossible (given certain views of time). (BTW: I don’t see how the “no infinity” option would help GRAUB, however.)
As for what option is best, I’m not sure. From my perspective, psr helps me make sense of why certain non-contradictory neighbors of a GR scenario are impossible (if certain recombination principles are true). On this option, some infinite sequences may be possible, as well as your case of the Asserters.
The “no infinity” option is a back-up option in my mind. The next backup after that is appeal to mystery.

Thanks for the clarification.
Regarding the psr, I’m not sure I get how it would apply. Do you think it might block some GR arguments, but not all?
As for the asserters, I’ve got a question. In the following argument, what premise(s) (if any) do you find unpersuasive?
Po. If time is possibly dense, then a contradictory GR scenario follows.
P1: If actual infinities are possible, infinitely many asserters are possible.Â
P2: If infinitely many asserters are possible, then time is possibly dense.Â
C: Actual infinities are impossible.

“that essentially makes Volos a zombie version of the Many Worlds Interpretation”

Right, but consider the alternative. According to Many Worlds each one of us experiences life in an unimaginable large number of parallel worlds. Each one of us is a mass murderer is some world. Each one of us experiences the Statue of Liberty swimming around Manhattan. Each one of us will live for ever. Itâs not only that Many Worlds violates OccamÂ´s dictum that one should not unnecessarily multiply entities (and as Volos proves itâs not necessary to believe that one exists in a vast number of versions). Itâs that Many Worlds moreover violates any sense of reasonableness. Thus the Volos interpretation by pushing most of the massive superposition into zombiehood maintains some semblance of reasonableness in one’s view of naturalistic reality.

“B1′ came from a path almost identical as B1, but just with some particles in slightly different positions at some earlier times. Yet, B1′ does not become conscious, but B1 does. Why?”

Well, scientific naturalism entails that our consciousness is some kind of expression of the physical brain. Now nobody knows what physical properties a brain must have in order to express consciousness. Nobody even knows how one could possibly investigate this question. Indeed it is not at all clear how the physical sciences might help, since the physical sciences do not require the consciousness hypothesis. Vis-Ã -vis the most important fact of all, the fact of our consciousness, scientific naturalism says practically nothing â despite all the posturing by Daniel Dennett and friends. Which is evidenced by the fact that nobody has any idea whether, say, cockroaches are conscious beings or not. Or how to ascertain whether consciousness is present in some physical system in the first place, no matter how it is produced. Having said all that, the scientific naturalist assumes that the physical properties which express consciousness are large scale ones. Which is not to say that a single electron may not make the difference. Perhaps a single electronâs transition from one state to another realizes the required large scale physical property of the brain and thus triggers the expression of consciousness. But since conscious states change every tenth of second or so, i.e. tenths of orders of magnitude slower than physical states, the scientific naturalist may safely assume that a significant shift in the physical state of the brain realizes that property and triggers the movement from non-consciousness to consciousness. In a detailed exposition of Volos the physical state of the universe changes with each Planck time e (about 10e-44 secs), but the mental state changes with E (about 10e-1), and thus the tagging algorithm which defines that state history of the conscious universe applies at multiples of E and not of e. Perhaps this answers your question.
But perhaps I am misunderstanding the question. Perhaps you refer specifically to the mechanism which according to Volos allows only the brain in exactly one state history of the universe to be conscious (even though it exists in a very slightly different state or even identical state in other state histories of the universe). In this case the answer turns on how you mean âwhy?â. If you mean it the sense of âhowâ, i.e. âwhy does nature pick the universe where B1 exists to tag as observable and the state of the universe where B1â exists to tag as unobservable, rather than the other way around?â – then the answer is âby chanceâ. It made no sense to speak of probabilities at t0-e, but it makes sense to speak of probabilities at t0 since at t0 there are complex (in the sense of âhaving the consciousness expressing physical propertyâ) brains in some states of the universe within the massive superposition, and thus now according to Volos nature randomly picks exactly one these states for âobservableâ status, thus turning all complex brains in it into conscious brains. But if you mean âwhyâ in the sense of âserving what purposeâ then of course this is a wrong question. The Volos metaphysics is a naturalistic metaphysics, and on naturalism reality evolves blindly without any purpose or reason or intelligence whatsoever.

“But if B1′ does not become conscious at t0-e, why does B1 become conscious at t0?”

That question appears to refer to the first paragraph in my comment above. In short, the scientific naturalist doesnât really know but assumes there is some significant physical property (namely the property of being potentially consciousness expressing) which B1â does not possess but B1 does. And, as we saw, the question should refer to t0-E not t0-e.

“Moreover, the matter of Boltzmann brains remains a difficulty, since much earlier than t0-e, say at t1, a Boltzmann brain BB1 existed in the superposition.”

Right, thatâs an issue to discuss. If one applies the Volos algorithm to Boltzmann brains some interesting properties arise.

Do you think it might block some GR arguments, but not all?
Yeah – the psr option may undercut P0 for instance (if an explanation in terms of a necessary rational foundation works; if that doesn’t work, then something in the neighborhood of C seems right).
BTW: do any or all of the following propositions come out necessary on your notion of necessary?
1. There are no people who transform into a prime number
2. Whatever is possibly the case is necessarily possibly the case.
3. Hurting a baby solely for fun is morally wrong.
4. Whatever has qualitative color has extension.
I’m thinking that all of these are metaphysically necessary but that none of them meet Swinburne’s criteria (in terms of its negation entailing a contradiction or rigid designation).
I bring it up because I wonder if our differing intuitions about the GR argument may ultimately turn on a different understanding of metaphysical necessity.

Nothing wrong with people transforming into prime numbers. Numbers are just entities jointly satisfying Peano or other axioms, and prime numbers just satisfy further constraints. For an appropriate choice of successor relation, people will be numbers (though you’ll need infinitely many people if all numbers are to be people), and there is no further difficulty about one of them being prime. 🙂

Right, but consider the alternative. According to Many Worlds each one of us experiences life in an unimaginable large number of parallel worlds. Each one of us is a mass murderer is some world. Each one of us experiences the Statue of Liberty swimming around Manhattan. Each one of us will live for ever. Itâs not only that Many Worlds violates OccamÂ´s dictum that one should not unnecessarily multiply entities (and as Volos proves itâs not necessary to believe that one exists in a vast number of versions). Itâs that Many Worlds moreover violates any sense of reasonableness. Thus the Volos interpretation by pushing most of the massive superposition into zombiehood maintains some semblance of reasonableness in one’s view of naturalistic reality.

A few points:
a. I disagree that Many Worlds is the alternative. It’s one alternative, and one with significant problems.
b. Also don’t understand Many Worlds as implying that each of us is a murderer in some world, etc.; the murderer would be a person very similar to me in many respects, but I would not be that person. The interpretation that we would be murderers, etc., seems to require some commitment to a view of identity that I don’t have.
c. Regarding Occam’s dictum, while collapse interpretations usually do not multiply worlds like Many Worlds, those views do not hold that collapse is just tagging some histories as unobservable. When I raised the objections that, on Volos, the Earth would not have existed, say, a billion years ago (or at some time before the first collapse), I was thinking of a usual view of collapse.
Given the tagging view of collapse, regardless of whether one uses the word ‘multiverse’ or ‘superposition’, the fact is that there is an ontological interpretation of all of those histories. That preserves the existence of the Earth, the Sun, etc., in the past, but at the cost of essentially including something that is no different from the Many Worlds multiverse, except in that those are worlds of zombies. So, it multiplies entities all around too, only that those are zombies.
d. Additionally, Volos, like other collapse interpretations, is less parsimonious in the sense that it includes more types of entities (zombies in addition to non-zombies).
e. I don’t think that a zombie multiverse has any semblance of reasonableness. I think the non-zombie multiverse is more probable, though still very improbable.
f. As I mentioned, if one does not have a likely interpretation, I think the proper answer is to recognize one does not know. I have no problem with that, and I take no stance on which interpretation is correct. More precisely, I don’t think the standard model is entirely correct; there are probably exceptions, once we include gravity and perhaps more forces (whatever makes the universe expands faster), but in any case, I make no claim that any of the pictures of reality given in QM interpretations is very close to reality.
g. As I mentioned, I think some modifications including collapse that does not require consciousness also are on the table. I don’t think they’re ad-hoc in a sense that is a problem.
Ad-hoc-ness is a problem because it (usually) indicates a theory with a much lower epistemic prior probability (given that it has to deal with specific details), and there is no experiment that raises its probability later (e.g., the universe was made to look like theory X predicts by a superhuman power; that’s empirically indistinguishable from X, but posits something much more complex).
On the other hand, an alternative to QM that supports a simpler or at least no more complex ontology, and makes the same predictions up till now, is in my view a serious contender, regardless of the intentions of those who invented it.
For that matter, if someone had come up with such a theory before someone came up with QM, the ‘ad-hoc’ reply would hold that we should reject QM because of that; I don’t think that the question of which theory is invented first or the intentions of its inventors play a significant role on assessing its probability (at least after the theory has already been presented).
So, I would take the position of ‘wait and see’ until experiments support one over the other.
Regarding B1 and B1′, I reckon I’ve been unclear; sorry about that. The issue is that B1′ exists in the superposition earlier than B1, yet it does not have any particles in different positions. Rather, it comes from a very similar history in which changes in electrons or other particles resulted in a brain with the exact same particles as B1, but just e earlier (‘e’ is just any very small time, not a Planck time)

But perhaps I am misunderstanding the question. Perhaps you refer specifically to the mechanism which according to Volos allows only the brain in exactly one state history of the universe to be conscious (even though it exists in a very slightly different state or even identical state in other state histories of the universe). In this case the answer turns on how you mean âwhy?â. If you mean it the sense of âhowâ, i.e. âwhy does nature pick the universe where B1 exists to tag as observable and the state of the universe where B1â exists to tag as unobservable, rather than the other way around?â – then the answer is âby chanceâ.Â It made no sense to speak of probabilities at t0-e, but it makes sense to speak of probabilities at t0 since at t0 there are complex (in the sense of âhaving the consciousness expressing physical propertyâ) brains in some states of the universe within the massive superposition, and thus now according to Volos nature randomly picks exactly one these states for âobservableâ status, thus turning all complex brains in it into conscious brains.

I think that talking about ‘nature’ picking stuff is a metaphor. The question is actually about causation.
But in any case, the question I was getting at is not how nature picks which state at t0 becomes conscious, but rather, how nature picks the time t0; more precisely, what’s the relevant difference that results in t0 being the first conscious state?
For instance, on Volos:
1. At t0-e, there was an evolved brain B1′ in a slightly different history, such that B1′ was identical to
B1 in terms of all of its particles.
So, how does nature pick t0 and not t0-e, or maybe t0-2e, etc., as the first time at which consciousness is expressed?
It’s not probabilistically, since there is no probability before t0, and there is no physical difference between the brains on QM.
A supporter of the MWI may say that all of those physically identical states are conscious, even if we do not know yet how consciousness starts. That’s no problem for MWI.
In other words, while MWI does not describe that some states are conscious and some are not, it does not posit states that are distinguished consciousness-wise, but not distinguished in any other way.
Similarly, someone proposing a modification of QM in which consciousness plays no role in collapse will have no difficulty with this.
Also, a decoherence histories interpretation has no problem.
However, Volos is committed to physically identical states (at least, to the best QM can tell), which are different from the of minds. One is conscious, the other one is not. Yet, Volos provides no explanation (not even a probabilistic one) as to why one of those states became conscious in the first place, but the others did not.
Perhaps, someone might suggest that particles aren’t indistinguishable after all, but that would be a modification of QM, and Volos is presented as an interpretation, not as a modification.
2. In addition, there is a plausibly even bigger problem regarding Boltzmann brains, for the following reasons:
i. Under the ontological interpretation that holds that all of the histories exist, even if only one of them contains consciousness, the problem of the Boltzmann brain comes to the forefront because at t1, much earlier than t0, there was a Boltzmann brain BB1 which was physically capable of consciousness. In fact, it seems that there was also a t2 How do I know I’m not a Boltzmann brain?
After all, it’s not more probable that I came from evolution (no probability in picking the first time), and there surely are unconscious brains, Boltzmann and the like, all around?
In other words, as soon as Volos is assumed, there appears to be no particularly good argument against the idea that I’m a Boltzmann brain. Appeals to parsimony or low prior probability do not work, because those appeals could only work before Volos is assumed. Once it’s assumed, then under that ontological picture, it seems I can’t even say that it’s improbable that I’m a Boltzmann brain.
As before, someone saying that collapse doesn’t need consciousness can argue that Boltzmann brains are very improbable. Decohence histories does not seem to have the same problem, either. I’m not sure what happens on MWI. But regardless of how other interpretations fare, Volos does not seem to have a way out.

And, as we saw, the question should refer to t0-E not t0-e.

I didn’t mean to use ‘e’ to mean a Planck time in that context, but just any very small time; sorry if that was not clear. But we can ask about E, and the issues arise anyway.

Yeah – the psr option may undercut P0 for instance (if an explanation in terms of a necessary rational foundation works; if that doesn’t work, then something in the neighborhood of C seems right).

Thanks; I’m not sure how you apply the psr, though. For instance, what premise of the argument against actual infinities I gave would be undermined?

BTW: do any or all of the following propositions come out necessary on your notion of necessary?
1. There are no people who transform into a prime number
2. Whatever is possibly the case is necessarily possibly the case.
3. Hurting a baby solely for fun is morally wrong.
4. Whatever has qualitative color has extension.

I’d say 1, 2 and 3 are necessary. I’d ask for clarification about 4. (I’d need more precision about the meaning of ‘qualitative color’?).
1. I would say it’s impossible by the meaning of the words, in my assessment; ‘prime number’ is an element with some properties in some abstract scenario, whereas a person cannot exist in an abstract scenario (meaning of the words).
Alternatively, we can consider the meaning of ‘transforms’; that seems to require a certain process with some causal connection between the end result and the beginning, and also some kind of continuity along the way, at least in some property.
But then again, if you consider the meaning of ‘prime number’ offered by Alexander, it’s possible. So, it depends on what one means by ‘prime number’, but in the end, the matter hinges on an issue of semantics.
I would say that 1* is necessary, for similar reasons to the ones above.
2. That has the difficulty of iteration of moral operators. I understand the rule as applying to the possibility of propositions involving non-modal terms, and then adding the formalism of iterating modal operators (or just eliminate the operators until only one is left).
So, let’s take P, defined in non-modal terms. If P is possible, then the meaning of the words is such that (even after considering rigid designators, etc.), it does not entail contradiction, and a contradiction (after considering rigid designators) seems to be entailed by stating that it does entail a contradiction.
Doing that manually is more complicated, and I would have to ask then how you define the operators.
3. The meaning of 3. sounds like ‘For all x, if x is an instance of torturing babies for fun, then x is immoral’, where ranges over all possible behaviors of personal beings (if the being is not personal, the claim is plausibly false), and the behaviors are described in non-modal terms (and are not morally evaluated in the description).
Given that 3 is true, it seems to me it’s necessarily true. If possibly Â¬3., then possibly an instance of such behavior is not immoral, which contradicts 3, so 3 is true iff it’s necessary (it’s kind of like iterating operators).
So, the question is whether it’s true. And it seems to me that we can assess that by means of our own intuitive grasp of the words, but with a rigid designation twist (e.g., under the assumption that a moral error theory is true at the actual world, it’s necessarily true, and 3 would be false, so what holds at the actual world does seem to matter).

I guess it depends on how much is packed into the notion of a contradiction. Here’s my candidate:
5. Nobody knows a false proposition.
It’s only a logical contradiction in a narrow sense if “knows” is short for something like “believes correctly with justification and …”, but it can’t be short for it, or it wouldn’t be a matter of philosophical dispute what to put in “…”.

Strictly speaking, how could the proposition that some person is a prime number (or that some bachelor is married, for that matter) be impossible “by the meaning of the words”? It’s not a proposition about words, after all.
And by the meaning of which words is the proposition impossible? The words “number” and “person”, let’s suppose. So, now, a Frenchman asserts: “Quelqu’une personne est un nombre premier.” The proposition that he asserted is the same proposition that we would assert with “Some person is a prime number.” We’ve supposed that the proposition in question is impossible by the meaning of the words “number” and “person.” But now our Frenchman asks something like: “Mais comment le sens des mots anglais ‘number’ et ‘person’ peut rendre impossible que quelqu’une personne est un nombre premier?” And surely he has a point: the meaning of English words has nothing to do with making it impossible for there to be a person who is a prime number.
OK, maybe you don’t believe in propositions. But whether there are propositions or not, the claim that (a) it is impossible that some person is a prime number is not a claim about language. So what should semantic claims have to do with it? Granted, the claim that (b) “Some person is a prime number” expresses an impossibility in virtue of the meanings of words. But (b) and (a) are different claims.

Angra,
I confess I don’t know what you mean by “by the meaning of the words”. ‘a person cannot exist in an abstract scenario’ is certainly not part of any normal definition of the word ‘person’.what premise of the argument against actual infinities I gave would be undermined? I was thinking P0.

Joshua,
I think there might be a misunderstanding here, so I’ll explain my take on this, and maybe if you explain me yours, we can make some progress (or at least realize what the difficulty is).
Regarding the word ‘person’, I don’t think we have definitions in a stipulative sense. Rather, we learn the meaning of the word by demonstration, as we do with most words describing concreta.
Then, a person who grasps the meaning of ‘person’ will be able to tell, for instance, that the proposition ‘The Earth is bigger than the Moon’ is not a person.
But similarly, when we learn the meaning of ‘abstract scenario’ (but here, there might be more than one meaning at play), we can tell that a person is not an abstract object, and an abstract scenario only has abstract objects as elements.
So, in short, it’s something we can tell a priori by means of our linguistic competence and logic (“a priori'” is not before everything, of course; we need to learn the words before that).

Strictly speaking, how could the proposition that some person is a prime number (or that some bachelor is married, for that matter) be impossible “by the meaning of the words”? It’s not a proposition about words, after all.

Okay, sorry if I was unclear.
I will try to clarify.
I mean that once one is linguistically competent, one can tell a priori that the proposition “some bachelor is married”) is false.
As much as I disagree with Craig’s defense of the Ontological Argument, his point about the concept of a married bachelor my help illustrate what I’m trying to get at (http://www.reasonablefaith.org/necessary-existence-and-the-ontological-argument )
I’m not saying that Craig agrees with my take on ‘metaphysically necessary’ (probably not), but just that his example of ‘married bachelor’ illustrates what I’m talking about. I will link to a more precise definition below.
Side note: I would disagree with Craig’s claim that the atheist needn’t maintain that the concept of a maximally great being (MGB) is like a married bachelor (though if she did have to, the theist is committed to claiming that all sort of other things are incoherent, etc.). She might say that, for all she knows (she need not take a stance), “A MGB exists” is more like “water is H2O2”, so one can’t tell a priori by means of linguistic competence and logic that it’s false, but nevertheless, if it’s actually false, it’s necessarily false (and that we can tell a priori).

And surely he has a point: the meaning of English words has nothing to do with making it impossible for there to be a person who is a prime number.

I would say that if a competent speaker can tell by logic alone that “a person is a prime number” (under the usual meaning of the words) is false, that falls in the ‘meaning of the words’ category I was talking about.
However, it may well be that some of the words in question have more than one meaning, in which case they express different propositions of course, and some of them might be possible, some of them might not (and clearly, if we redefine the words as we please, any sentence can express something possible or impossible).

OK, maybe you don’t believe in propositions.

Not in an ontological sense (i.e., I wouldn’t include them in an ontology), and the same goes for numbers, etc., but I have no problem saying that a proposition is true, or that the number 5 is prime, so no problem there.
I hope I’ve clarified what I was trying to say.

OK, maybe you don’t believe in propositions. But whether there are propositions or not, the claim that (a) it is impossible that some person is a prime number is not a claim about language.
So what should semantic claims have to do with it? Granted, the claim that (b) “Some person is a prime number” expresses an impossibility in virtue of the meanings of words. But (b) and (a) are different claims.

I’m not sure I’m tracking here, though the claim that it’s impossible might be taken to be partially a claim about language (the “aboutness” is a sticky issue, though), if by ‘impossible’ one means something like ‘contradictory after one counts the meaning of the words, including rigid designators’, in the sense of ‘meaning of the words’ explained above:
In any case, a more precise definition is found in a paper by Swinburne (on page 12 of his paper “What kind of necessary being could God be?” http://users.ox.ac.uk/~orie0087/framesetpdfs.shtml ); I do not agree with his take on essences (I’m not an essentialist), but if I get his point correctly, I do agree with that definition of metaphysical necessity.
Granted, you may well disagree about what ‘metaphysically impossible’ means; I guess a possibility would be to try to see how we learn the meaning of ‘impossible’, and see if we can figure out what it means; if everything fails, it might even be that Swinburne’s “common language” assumption is mistaken, and we’re using the concept of ‘impossible’ differently.

It is interesting to observe how philosophical discussions quickly turn to the fundamentals. Itâs like a universal force of philosophical gravity applying.
Iâd like to throw one more idea into the soup and see if something good comes out.
Probably we all agree that there are meaningful and meaningless sentences, and that only meaningful sentences may be true or false. Thus truth value is a property of the meaning of a sentence and not of the sentence itself. But then it is a waste of time to debate the truth value of a sentence unless there is some evidence that people agree on its meaning. Weâd better find a way to ascertain that we share the same meaning before debating the truth value of a sentence. Even when thinking by oneself about a sentence itâs a good idea to first think about what that sentence means. Socrates would surely agree.
Iâd like to propose the following principle: âAll meaning is grounded in personal experience.â One way in which the meaning of that principle is grounded in personal experience is this: In our experience we find that most words refer (or have meaning which refers) to shared facts of the human experience (e.g. âflowerâ, âhopeâ, âwillâ, âbeautyâ, âcolorâ, âtimeâ, âthreeâ, âlargerâ, etc). Conversely, unless there is some common ground in two personsâ experience of life, no communication between them seems to be effective, because there is no common ground for epistemic traction. Thus, if a participant in a discussion cannot *describe* to another how a particular sentence relates (even in the most tenuous way) to the shared experience of life the others will have no idea what she means by that sentence.
And hereâs my problem. I can relate to personal experience the sentence âIt is a priori true that there are no married bachelors.â But I have no idea how Joshuaâs #1 âIt is metaphysically necessary that there are no people who transform into a prime numberâ relates to personal experience. I donât even have an inkling how the simpler âthere are people who transform into a prime numberâ may relate to personal experience, and thus have no idea what it means, or even may perhaps mean. I find I can relate individual words in that sentence with my experience of life, but cannot relate that particular string of words with my experience of life. And I challenge Joshua or anybody else to describe to me how this sentence relates to our common experience of life, and if it doesn’t why we should think about it.
My larger point is that the principle above serves as a philosophical reality check. If one doesnât know in what way a sentence relates to oneâs experience of life, then one doesnât know what that sentence means (under the above understanding of âmeaningâ), and thus it makes no sense to think about its truth value. Or, in other words: If one doesnât know how a sentence relates to oneâs experience, then one also doesnât know how that sentence being true or false relates to oneâs experience â but then why worry about whether that sentence is true or false? If one values oneâs time and doesnât want to waste oneâs thoughts or discussions in useless speculations, then one must embrace the above understanding of meaning (or perhaps a more specific understanding which comports with it).

Thanks Angra; those are good thoughts.
I would carve a deeper distinction between epistemology and metaphysics. Some reasons:
First, if ‘@’ rigidly designates the actual maximal, consistent state of affairs, then one of the following two propositions is necessary: (i) if @ obtains, then there are an even number of protons; (ii) if @ obtains, then there are an odd number of protons. But no one can discern either (i) or (ii) a priori.
Second, it seems to me that whatever is possible is necessarily possible. From this premise we can show that one of the following claims is necessary: (i) there are necessary abstracta; (ii) there are no necessary abstracta. But I’m not sure what it means to say “we” can tell (i) or (ii) is true a priori.
Third, I am not sure what “can” means in “we can tell a priori that X”. Does it get an epistemic definition, too?

Dianelos,
I would like to ask for some clarification on the proposed principle; I’m not entirely sure I understand what you mean by it.
That aside, I tend to agree (if I understand your point correctly) with your point that “Â if a participant in a discussion cannot *describe* to another how a particular sentence relates (even in the most tenuous way) to the shared experience of life the others will have no idea what she means by that sentence.”, at least if ‘most tenuous way’ is taken to encompass indirect means, e.g., to allow for communication between sufficiently advanced intelligent.
On the issue on the prime numbers, your question raises an interesting (to me) point.
If I say (using the words in the usual sense) “Yesterday, Alice saw the (positive) square root of 3 floating in the air”, is that sentence meaningless, or meaningful and false?
Of course, it may be true if we’re talking about a representation of the square root of 3 (say, written on a balloon), but let’s say that we’re talking about the square root, not of a representation of it.
The following is tentative. but my attempt to understand that sentence (and hence, conclude it’s false, or more precisely that it expresses something false) would be as follows: The sentence means that Alice saw an object on the street, say X. It also says that the object was a the square root of 3. But using my grasp of the expression ‘square root of 3’, I conclude that whatever Alice saw on the street does not meet any criteria for being the square root of 3 (to any degree, if there were fuzziness, though in this particular case I don’t know there is), so the sentence would be false (i.e., expressing something false).
At least going by my intuitive understanding of ‘prime number’ (Alexander may understand the expression differently), ‘people’ and ‘transform’, I can similarly come to the conclusion that the claim is false.
So, I would imagine the scenario as follows: at some time t0 there is a person (say, Bob), who then undergoes a certain process of change (it can be very fast), such that there is kind of causal or ontological continuity at any point in the process (i.e., at least, some of the things Bob or the following things in the process are made of continue to exist from one stage in the process to the next, if there is no temporal density, and for a small interval if there is, or at least there is some causal continuity).
The specific kind of causal or ontological continuity that is required is very difficult to characterize, as is a conceptual analysis of the term ‘transforms’ (in the relevant sense, which is not the sense of mathematical transformation I think); maybe ontological continuity is required always, but in in any case, the issue is that at the end of the process, instead of Bob, what we have some other entity.
Now, the sentence says that the entity in question is a prime number. But given the scenario I constructed, I can tell using only my grasp of the language (again, Alexander may use the word differently) that the entity in question is not a prime number, pretty much in the same manner in which I can tell that what Alice saw on the street is not the square root of 3.
At least, that would be my tentative way of understanding what the sentence means, and why it’s false. And it would come out as necessarily false, on my understanding of necessity.

Joshua,
Thanks for your reply. I’ll try to clarify the best I can.
1. On the issue of the protons, I think they may both be false (maybe there are infinitely many protons, and that would make it false at least under my understanding of ‘even’ and ‘odd’), but nitpicking aside, I’m not claiming that we can always tell that some proposition is metaphysically necessary only by logic and our intuitive grasp of the language.
Rather, in my reply to your previous post, I was explaining what I was trying to explain what I meant by “by the meaning of the words”, since that expression was a sticking point.
In some cases, we can actually tell, using only logic and our intuitive grasp of the words, whether a proposition is true or false, and that’s a sufficient condition for its being necessarily true or false.
But it seems to me it’s not a necessary condition for that, as the ‘Water is composed of H2O’ example shows. It’s what Swinburne calls ‘uninformative designators’.
2. I don’t know about ‘necessary abstracta’. I have to ask what you mean, more precisely.
If you’re talking about a proposition like, say, “The number 5 exists”, then a question is “what does that sentence means”?
If it’s an ontological claim, I would deny it. But I would not deny that if we’re talking about the abstract scenario ‘natural numbers’ the claim is true of that scenario (surely it is).
Analyzing the meaning(s) of ‘exists’ in the context of mathematics, etc., or ‘there are’ when we say that there are true propositions (for instance) is not an easy matter, but I don’t think that, in ordinary usage (including ordinary usage by mathematicians doing math, etc.), those are ontological claims.
3. Yes, it means that an agent who understands the meaning of the words (including a number of related words, if needed) and logic and has sufficient intelligence is able to decide the matter, based on that alone and without empirical data.
But to be clear, I do not claim that such condition is required for a proposition to be something to be necessarily true (or possible, or impossible, depending on the case). It seems plausible that it is not. But it is a sufficient condition.

Swinburne works in terms of sentences, and even talks of sentences being logically necessary. But sentences are logically necessary only in a derivative way: their necessity derives from the necessity of what the sentences express.
Here is an argument. Consider these two sentences (and excuse my poor French):
1. Il est necessaire que deux plus deux egale quatre.
2. It is necessary that two plus two equals four.
The two sentences express the very same truth. But on the view that necessity is at base the necessity of sentences, 1 and 2 really are something like:
1. La phrase ‘Deux plus deux egale quatre’ est necessaire.
2. The sentence ‘Two plus two equals four’ is necessary.
But it is clear that while (1) and (2) both express truths, they do not express the same truth.
Moreover, the necessity of propositions should not be a function of accidents in how we came to have the vocabulary to express these sentences. Take “knows” (in the central sense; I am excluding “he knows many things that ain’t true”). It is uncontroversial among competent speakers of English that “x knows p” commits one to p being true. It is more controversial that it commits one to one’s having a belief that p or that it commits one to having justification that p. And whatever further conditions a full account of knowledge will need to have are yet more controversial.
But all of these conditions on knowledge, if they are there at all, are metaphysically on par. It is no less necessary that if x knows p, then x has justification with respect to p (assuming that this conditional is supported by the correct account of knowledge) than that if x knows p, then p is true. It is a mere accident of how we got to having the concept of knowledge that the latter is utterly clear and the former is not.

Alexander,
Thanks; those are very interesting points.
Regarding when sentences are necessary, I tend to agree with Swinburne’s definition (if I get it right), except for the fact that I have no ontological commitment to essences of beings (which is kinda lurking in the background in his use of the words).
As for his take on propositions, I partially agree with him, but I think I disagree partially; I’m not entirely sure because part of what he says about them is not entirely clear to me (more on that below).
With respect to your examples, as I mentioned earlier, I don’t have a problem with talk about propositions, or with saying that a proposition is necessary. In your example, 1 and 2 appear to be about propositions, whereas the other 1 and 2 below are about sentences.
Swinburne considers propositions a kind of fiction, but says “there no reason to deny that ordinary talk about ‘propositionsâ’ (of a kind that does not imply their eternal existence) can be analyzed as talk about human sentences.”
Yet, he does not define ‘proposition’, or necessity, etc., in terms of propositions, so we would need to extend the definitions in order to analyze talk of propositions as he proposes. So, perhaps this ‘fiction’ may be defined as ‘that which is expressed by a sentence’, or something like that.
If so, it seems to me that his definition of necessity (and possibility, impossibility, etc.) might be extended to propositions, saying that a proposition is necessary (possible, impossible) if it’s expressed by a necessary sentence.
Given that, 2. would mean “That which is expressed by the sentence is necessary”, and 1. would mean the same, since “deux plus deux egale quatre” means the same as “two plus two equals four”, and they would both be true.
So, the extended analysis seems to work at least in that case. But it’s tentative.
Regarding your second point (i.e., the “moreover”), I’m not sure how those accidents would affect the necessity of propositions on Swinburne’s account. Some propositions may be controversial, but that does not seem to make the proposition (or the sentence) contingent, on Swinburne’s account, as far as I can tell.
It seems similar to the question of whether a certain formula follows from some axioms. Ascertaining whether it’s true might be very difficult. But that does not mean that it’s not necessarily true that it does (if it does).
Maybe you’re objecting to the idea that we can tell a priori, since sometimes the matter is too complicated for humans to tell (either a priori or not)?
If so, in my latest reply to Joshua above, I specified “sufficient intelligence”, to cover such cases. Maybe that wasn’t clear enough.
I’m not sure what Swinburne’s take on the matter is.
Still, there is the issue of how to characterize metaphysical modality in case we consider propositions to be the primary bearers of modal properties, and we also consider that there are propositions which cannot be expressed in any language, human or otherwise.
That is not entirely clear to me. Perhaps, a partial approach would be that for propositions that can be expressed, Swinburne’s definition holds. But for other propositions, it’s a difficult question of conceptual analysis.
The question seems to be: What does it mean to say that a proposition not expressible in any language is, say, impossible?
It’s not something that people say colloquially, so it seems to be a technical term. But no definition has been provided, and philosophers do not seem to agree on the meaning, so it’s difficult to say.
All that aside, and just to (hopefully) clarify some of my views a little bit, personally I don’t include numbers, propositions, etc., in an ontology, but I’m not sure I would call them ‘fictions’, since the word ‘fiction’ might have a meaning such that it denotes some specific sort of scenarios, and which may not include propositions, numbers, etc.
Also, I disagree with some fictionalists about, say, numbers, who say that 2 + 2 = 4 is not true, but a fiction. I think that 2 + 2 = 4 true, though I also (if I’m implicitly or explicitly talking about things in the scenario ‘Star Wars’) I think it’s true that Darth Vader is Luke Skywalker’s father, even if it’s a
fiction (i.e., true in a fictional scenario does not entail false as I see it; it’s still true).
I don’t know what Swinburne’s position on that is. If he takes the extreme view that 2 + 2 = 4 is not true (but I get the impression that he does not), I don’t agree. And the same goes for propositions.

It’s not something that people say colloquially, so it seems to be a technical term. But no definition has been provided, and philosophers do not seem to agree on the meaning, so it’s difficult to say.

Clarification: I mean that no commonly accepted definition has been provided.
It seems Swinburne provides a sort of definition (page 18), though it’s not clear to me what and informative or an uninformative designator might be in a proposition that cannot be expressed in any language…

“there is no reason to deny that ordinary talk about ‘propositions’ (of a kind that does not imply their eternal existence) can be analyzed as talk about human sentences.”
Certainly, there are *some* reasons: try these (at section 2).

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But no need to argue the point here, I think, since I do agree with you that there are some reasons, because I can think of some reasons, like psychological factors limiting human cognition (but maybe some aliens could go beyond that, so what if we extend it to ‘any language’, not just human language? So, one question is whether extending it to any language would get around that), or like size/cardinality considerations (though even if a fixed human language can only talk about a denumerable number of some stuff S (numbers, propositions, etc.), we can use the same symbols in different contexts to mean different stuff).
So, I agree that there are some reasons (maybe he meant that upon further consideration, there are no such reasons). Some questions are whether those reasons are decisive, whether extending the definition to any language (human or not) works around them if they are, etc.
Those are complicated matter, but while I agree with Swinburne when it comes to sentences (i.e., at least as I understand the words, that does seem to capture the meaning of ‘impossible’, etc.) and also propositions expressed by sentences in a human language, I’m not convinced by his claims that sentences are primary bearers; propositions may well play that role in my view, since I don’t have a problem with properties of things that I don’t include in an ontology, like natural numbers or even objects in impossible scenarios.
So, let’s say for the sake of the argument that the primary bearers of modal properties are propositions. Then, we still need to (well, I do, so I’ll say ‘I’ in case others already got it) figure out what modal terms mean, and what ‘proposition’ means.
So, I may start with modal properties. There is no agreed-upon definition of them. Also, colloquially, terms like ‘impossible’ are used in several different ways. For instance, many would say it’s impossible for me to jump from London to New York on a single bounce, and that seems true under some common usages of ‘impossible’.
So, I still need to learn what they mean in philosophy. And I get some paradigmatic cases as a means of grasping the terms. In the case of ‘metaphysically impossible’ (to pick one of the terms to simplify) Those cases seem to involve one of the following:
a. Contradictions, such that the contradiction can be established by the form of the sentences expressing the proposition in question (e.g., A&Â¬A, or more complicated ones, and then some sentence replacing “A”).
b. Contradictions not in a., but such that the contradiction can be established after considering the meaning of the terms, and determinable a priori (e.g., There are married bachelors).
c. Contradictions not in a. or b., but such that the contradiction can be established after considering rigid designators, informative or not, in the sentence expressing the proposition.
d. I have no paradigmatic case of propositions that can’t be expressed in human language, but I can extend the idea to any other language, human or not.
e. I have difficulty understanding the idea of a proposition that is not expressible in any language at all, so I’ll leave the matter for later.
So, based on those cases, I (hopefully) grasped the meaning intuitively, and I can also propose necessary and sufficient conditions for a proposition to be impossible, at least when the proposition is expressible in a language (any language), and that would be when it’s expressible by an impossible sentence, in the sense the previous conditions a., b., and c. indicate (i.e., in Swinburne’s example).
That still isn’t a hypothesis about what it means for a proposition to be impossible, because:
a. If we assume that propositions are the primary bearers of modal properties, then there is something more fundamental that the previous necessary and sufficient conditions do not capture.
b. That’s surely the case if there are propositions not expressible in any language.
Even so, the above proposal of necessary and sufficient conditions appear to capture, as far as I can tell, the way in which I go about figuring out whether a proposition is impossible, so perhaps, the assumption that propositions are the primary bearers is mistaken.
Alternatively, perhaps I can actually modify those conditions proposed as necessary and sufficient for the case of propositions (i.e., eliminating any reference to sentences), like Swinburne does on page 18 under the assumption that propositions (of a kind I’m not even accepting for the sake of the argument here, though I might if needed) are the primary bearers.
That attempt, however, has a difficulty. I’m having difficulty understanding rigid designators, informative or otherwise, without sentences in some language, human or not. So, I’ll need to give it more thought.
For now, if propositions are primary bearers, at least I have a proposed method for ascertaining impossibility of propositions expressed in human language (at least in cases in which I have enough brain computing power to figure it out), and which seems to capture my actual intuitive method for figuring it out, as far as I can tell, and proposed necessary and sufficient conditions in cases in which a proposition is expressible in some language.
So far, more or less so good.
Yet, I can see that there are philosophers who hold that metaphysical impossibility is not that, and that even for some propositions expressible in human language, there are impossibilities not captured by the previous conditions.
But I’m not sure how to learn their terms. In the cases I’ve encountered, they don’t define metaphysical impossibility in terms of simpler notions I do understand. Rather, metaphysical impossibility (or rather, metaphysical possibility, but impossibility is just its negation, so if I have the notion possibility, I get the notion of impossibility easily, and vice versa) is taken as primitive (see note 5 in Swinburne’s paper, page 22).
On this point, I seem to be in a situation similar to Swinburne’s, since considering it primitive does not help me grasp the meaning of the term. My attempt to grasp the meaning of ‘metaphysically impossible’, by paradigmatic cases, led me to something like the above, and nothing more.
Nor do I get other set of necessary and sufficient conditions, or at least sufficient conditions, that I could use to check for impossibility of propositions that I encounter.
So, at this point, it seems to me that perhaps, it’s time to give up the ‘common language assumption’ that Swinburne made. Maybe there is no common language after all. Maybe the concept of ‘metaphysically impossible’, that I got from the examples (and possible, necessary, etc.), is not the same concept some, even many philosophers got.
What to do?
In ordinary cases, if the ‘common language assumption’ fails, that might be because a person has not seen enough paradigmatic cases; in that case, a solution is to look for more such cases. But I’ve already done that. Moreover, this is supposed to be a concept grasped by the population at large, and most people have had contact with a lot fewer examples than I have, and pondered about the matter a lot less (or rather, not at all), so I’m not sure how else to proceed from here.
Joshua, any ideas, comments or suggestions are welcome. If you have learned the concept in a different way, please let me know how.

‘Given that, 2. would mean “That which is expressed by the sentence is necessary”, and 1. would mean the same, since “deux plus deux egale quatre” means the same as “two plus two equals four”, and they would both be true.’
“That which is expressed by the sentence s1 is necessary” means something different from “That which is expressed by the sentence s2 is necessary”, even if in fact s1 and s2 express the same thing. (Compare: “What Bill says is true” and “What Jane says is true” mean different things, even if Bill and Jane say the same thing.)
Maybe some fictionalist semantics might help here.
It seems to me that philosophy is full of propositions such that either the proposition is necessary or its denial is necessary, it’s controversial which is which, and neither’s necessity can be determined solely by the meanings of words or rigid designators.
Here are some such examples:
1. There are necessities that aren’t linguistic or based on rigid designators.
2. There are (in the ontologically beefy sense) properties.
3. There are numbers.
4. There could be tropes.
5. Truth supervenes on being.
6. There are negative states of affairs.
7. Nothing causes itself.
8. Some object could have had a different causal history of its existence.
9. Moral properties supervene on nonmoral properties.
10. There are objective aesthetic truths.
11. Causation is grounded in the arrangement of objects.

“That which is expressed by the sentence s1 is necessary” means something different from “That which is expressed by the sentence s2 is necessary”, even if in fact s1 and s2 express the same thing. (Compare: “What Bill says is true” and “What Jane says is true” mean different things, even if Bill and Jane say the same thing.)

Okay, you’re right. What I had in mind (but I see I misspoke; I shouldn’t have used the quotations as I did) was that “The proposition that two plus two equals four is necessary” would mean that (which is the proposition in question) is necessary, but the sentence would be used only to establish the content, not as part of the quotation. It would be like saying What says is true, and the same for Jane.
In order to ascertain the meaning of 1 (or 2), one would first need to see what is expressed by the sentences in question.

It seems to me that philosophy is full of propositions such that either the proposition is necessary or its denial is necessary, it’s controversial which is which, and neither’s necessity can be determined solely by the meanings of words or rigid designators.
Here are some such examples:

Even though they’re controversial, it does not seem to me that the way to try to settle it is other than analysis of the concepts (including empirical evidence if needed) and logic, at least as I understand the terms (see my immediately previous reply to Joshua).
In order to find counterexamples (at least, as I understand the words) I would need to find cases in which it seems to me that an impossibility (for instance) would not be one of those a., b., or c., in my reply to Joshua.
The problem is, however, that when I try to assess whether something is metaphysically impossible, I seem to check just that. In other words, upon reflection, when I’m assessing whether something is metaphysically impossible, it seems I’m trying to find contradictions in one of those matters.
So, it seems to me that not only are those alternatives (regarding metaphysical impossibility) exceptionless by the way I use the terms, but moreover, that seems to be how I actually grasp the term ‘metaphysical impossibility’.
That’s why I mentioned that there might be a problem with the assumption of a common language, but I have no way around it.
I’ll try to assess your cases below, but first a general point: in all cases, I think the concepts are rather vague, and a procedure to try to answer the questions would involve analysis of those concepts, which would take a lot more time and effort than I could properly dedicate to them here.
Given that, I will not attempt to answer all of them, but just to sketch my take on them as an example, but in any event, pointing out that the way in which I would proceed to try to ascertain whether they’re true would be conceptual analysis (including, if needed, rigid designators) and logic.
However, I realize that you may have a different procedure, and perhaps that might help me grasp the meaning of the modal terms as you use them, so I would like to ask how you would go about trying to figure out whether they’re necessary, or impossible (or neither; see below).

1. There are necessities that aren’t linguistic or based on rigid designators.

It’s not entirely clear to me whether under “linguistic or based on rigid designators” you include also contradictions in which you don’t even need to take a look at the meaning of the words.
If you’re including them, I disagree for the reasons I’ve been explaining, but the matter is also a matter of conceptual analysis.
In other words, reach the conclusion that the claim is [probably] false on the basis on logic and conceptual analysis alone; if I’m wrong, okay, but I don’t see that claim as counter evidence.
The matter is no doubt controversial, but then, similarly it’s sometimes difficult to tell whether a formula follows from some axioms; when things like the meaning of the words enter the picture, that further complicates matter.

2. There are (in the ontologically beefy sense) properties.

As before, the ‘ontologically beefy’ sense is not entirely clear to me. But if it requires some entity instantiating them, then given that it’s metaphysically possible in my assessment that there are no entities (I’m talking about concreta; I don’t consider abstracts entities), then I conclude it’s not necessarily true, and on the basis of conceptual analysis and logic…unless there is some contradiction I’m not seeing, with some rigid designator picking some property like omnipotence that has modal entailments.
But I think that that would probably be a wrong definition of ‘omnipotence’, and at any rate I believe there is no being with the power to rule the universe, anyway, so even then, I would say that 2. is not necessary.
At any rate, even if I’m wrong about 2., I would say that I’d be wrong probably due to some contradiction I missed in one of the aforementioned ways.

3. There are numbers.

It’s true that there are infinitely many primes, but when I assert that I’m implicitly thinking of the set of natural numbers as my domain of discourse; so, yes, it’s necessary that there are infinitely many primes (and hence, infinitely many numbers) in the set of natural numbers. I can tell that by the meaning of the words.
But if the matter is (as I think it is) an ontological claim, then the question is whether the concept of ‘entity’ and ‘number’ are compatible. If it is, then that would be possible, but I doubt necessary (so, in that case, I would disagree with the view that either the proposition or its denial is necessary). If it isn’t, then it’s impossible.
However, the word ‘entity’ might not be precise enough; maybe different people are using it differently, in which case I’d say that there is no objective fact of the matter (in the colloquial sense of ‘there is no objective fact of the matter’, which I means is not about mind-independence), or more precisely, it depends on what one means by 3.

4. There could be tropes.

In an ontological sense?
I think probably not, but essentially the analysis is as in 3., mutatis mutandi.

5. Truth supervenes on being.

I’m not sure I understand that. If it entails that propositions or in any case truth-bearers need to be included in a correct ontology, I tend to disagree (but as before, see 3.).

6. There are negative states of affairs.

As in other cases, I’d say that (for instance) the state of affairs that my keyboard is not green obtains, but I’m not making an ontological commitment to anything beyond the fact that my keyboard is not green.
Else, the matter is about the meaning of words like ‘entity’, etc.; the points are as before.

7. Nothing causes itself.

It seems to me that infinite causal regress is possible; if so, let’s consider all of causal reality in a scenario in which there is such regress.
A question is: does it cause itself?
I would say that the causes are all there; if we consider the whole of causal reality as a ‘thing’, then it depends on what one means by ’cause’. I tend to think that ordinary terms like ’cause’ and ‘thing’ are probably not precise enough to tell, but in any case, the issues to be resolved is about whether the words ‘thing’ and ’cause’ would apply…ifinfinite causal regress is possible.
But is it possible?
Clearly, there is no contradiction, and I don’t think there is any contradiction by considering the meaning of the words, at least not considering rigid designators, so plausibly it is…but the word ‘time’ might include such designators (it’s a case in which even whether there is a rigid designator is difficult, at least for me), and if so, perhaps things like temporal density and infinite temporal regress might be ruled out if they don’t obtain in the actual world (issues on which I take no stance), and plausibly causal regress too, if there is some sufficiently strong conceptual connection between time and causation (which is debatable, but also a matter of conceptual analysis).

8. Some object could have had a different causal history of its existence.

As in other examples about, this one seems to be a case of lack of conceptual precision, in this case about the word ‘object’, which might be used in different ways. So, maybe the answer is ‘no objective fact of the matter’, or ‘it depends on what one means’, but in any case, even if the concept is precise enough, it is a matter of analysis of the meaning of ‘object’ and the other potentially difficult words, as far as I can tell.

9. Moral properties supervene on nonmoral properties.

My take on that is that that’s necessary, and I would assess that based on an analysis of what we mean by moral sentences.
But if I’m in error, that would still be the result of erroneous conceptual analysis as far as I can tell. I don’t know how else to go about that.

10. There are objective aesthetic truths.

And to make it more controversial, I don’t think that “there is an objective fact of the matter as to whether that painting is beautiful” (for instance) is a claim about mind-independence, at least in the senses of mind-independence in which I’ve seen it used.
So, if we’re talking about ‘mind-independent properties’, I would have to ask for clarification about the technical term ‘mind-independent’, whereas if we’re talking about whether there is an objective fact of the matter as to whether, say, painting A is more beautiful than painting B (for some A and B), I would tentatively say that sometime there is, and sometimes there is not; it would depend on the paintings…but in the end, this too rests on an analysis on the meaning of ‘beautiful’, and a (plausible) empirical observation about similarities in the minds of humans.

11. Causation is grounded in the arrangement of objects.

I would ask about the meaning of ‘grounded’, since that seems to be a potentially vague term with more than one technical meaning, but in any case, I wouldn’t proceed in any different way.
Anyway, as I said, discussing those cases would take way too long. What I would like to ask, in the context of the issue of the meaning of terms like ‘metaphysically impossible’, are things like how you learned them, and how you would go about trying to ascertain matters such as the above (for more details, please see my immediately previous reply to Joshua).

Angra,
a. It is an embarrassment that after 80 years scientific realists do not agree on what the best realist understanding of QM is. Actually there is no discernable move towards agreement. As Nick Herbert writes in his book, the best kept secret in science is that physicists have lost their grip on reality. And after 80 years and after QM has proven the by far most complete and productive scientific theory of all time, physicists do not appear to have regained any grip on reality. Doesnât look good for scientific realism.
b. I agree with your sense about personal identity, but hereâs the problem the scientific realist faces: Consider the state of the universe in which you are right now reading this post on your computer. According to scientific realism blind physical forces will move the state of your brain into its next states, QM defines all the state transitions your brain may undergo, according to MWI all these state transitions obtain in some state history which branches out from the current state, and finally on MWI all these state histories are as real and actual as any other. As it happens in a small proportion of these branches your brain will realize states of murderous action. I donât see how on scientific realism you are justified to claim this person in that state history is not you. From the scientific realismâs point of view it certainly is you. After all, the physical body of that murderer is a causal continuation of your body right now, and its brain has autonomously decided to murder people. So it seems that your and my understanding of personal identity is not compatible with the metaphysics of the many worlds interpretation.
c. Volos is more parsimonious in that it does not multiply minds. It is less parsimonious than Copenhgen in that it maintains the reality of the entire massive superposition. On the other hand it keeps physical reality objective and mind-independent, whereas Copenhagen doesnât. Rereading portions of Herbertâs book I see that the original Copenhagen interpretation is an epistemic one. According to Bohr there is a unknowable quantum domain and an unknowable classical domain and QM describes the interface between the two. Von Neumann and his followers have worked on an ontological Copenhagen interpretation where collapse takes place, and found themselves making consciousness the cause of the collapse, thus rendering physical reality non-objective.
d. In that sense it is less parsimonious than MWI.
e. A zombie universe is by definition a reality nobody will ever experience, and is therefore cognitively vacuous. No conscious being cares what may be the case or is the case in a zombie universe, since it will not affect one or any other conscious being in any sense whatsoever. Thus the fact that in some zombie universe the Statue of Liberty swims around Manhattan produces (at least in my case) no cognitive stress whatsoever. But it deeply bothers me to think that on many worlds I, and many others like me, observe the Statue of Liberty behaving in such unbecoming ways. Clearly absurd states of affairs are much more disturbing in universes where conscious beings observe them. And since what is absurd and what isnât is grounded on experience it arguably doesnât even make sense to speak of absurd states of affairs obtaining in zombie universes.
f. QM has grown by leaps and bounds without in any way modifying its basic structure. Everybody expects gravity to find its place within QMâs structure. So, probably, QMâs structure is here to stay. Whatâs more relevant though is this: One can explain the difficulty of describing a physical reality that will produce quantum phenomena without going into the details of the theory itself, but only discussing the relevant phenomena (observational facts) the theory has uncovered. These are here to stay whatever may happen to the theory in the future. A case in point is Bellâs theorem and the proof that reality is non-local, which can be demonstrated using only a small set of observational facts.
g. Well, science is about finding the simplest description of phenomena. The various âcorrectionsâ of quantum theory (such as GRW or Weinbergâs suggestion) are not simpler theories, but add stuff to the original theory. If they were simpler they would stand on their own (and probably earn their creator a Nobel). But the scientist is supposed to be objective, and *not* add stuff to a scientific theory only in order to make it compatible with her metaphysical assumptions. I think thatâs a no-no in the scientific method.
This point apart, I claim that Berkeleyâs subjective idealism provides a self-evident, simple, intuitive, and problem-free ontological interpretation of QM. (And as a bonus explains human free will.) Only it does not comport with the intuitions of the scientific realist. Itâs not QM is that is weird, but the conjunction of QM and scientific realism.
Regarding B1 and B1â they being physically identical, B1â obtaining earlier in the massive superposition within a different state history:
The mechanism (or algorithm) which on Volos determines the properties of reality works as follows: At each time which is a multiple of E one (if any) of the not already âunobservableâ states of the universe in which complex brains exist becomes âobservableâ, and the complex brains in it express consciousness. All other states at this point in time as well as all states in future branches of them in the massive superposition become âunobservableâ, which means that the complex brains in them will not express consciousness (remain zombies). (As you see I tried to describe how reality is according to the Volos interpretation without using metaphorical language which one may misinterpret as entailing some kind of external or non-physical guiding hand. Volos does entail a causal connection between states in the massive superposition though.)
Thus, if B1â exists in a state of the universe which becomes âobservableâ then that brain will express consciousness. If the later B1 exists in a state which will be marked unobservable, then B1 will not express consciousness even though it is physically identical to B1â. Zombie brains are physically identical to non-zombie brains. If the later B1 exists in some branch that grows out from the state of B1â then its state will perhaps become observable and B1 too will express consciousness. State histories may contain identical brains at different points in time, and thus it is possible (though unlikely) that exactly the same consciousness will obtain at two different points in time within the unique conscious state history.

How does nature pick t0 and not t0-e [where B1â is present in some state] at the first time consciousness is expressed? It’s not probabilistically, since there is no probability before t0, and there is no physical difference between the brains on QM.

The point in time at which the first brain will express consciousness is deterministically fixed. At this point in time though indeterminism kicks in. Perhaps there are several states where complex brains exist, and in this case only one of them will randomly become observable. Suppose, for example, that at the very first time tâ where complex brains evolve there are four states with such brains, namely: {B1â}, {B1â, B2â}, {B3â}, {B2â, B4â}. Only one of these states will randomly become observable. If this happens to be the fourth state then the first conscious brains will be B2â and B4â, and the first state in the unique conscious state history within the massive superposition will be {B2â, B4â}. The other three states as well as all their future branches will become unobservable.
Itâs true that MWI does not add to reality my dual property of observable/unobservable. This is the price Volos pays to avoid MWI many absurdities.

Yet, Volos provides no explanation (not even a probabilistic one) as to why one of those states became conscious in the first place, but the others did not.

But it does. On Volos one of those states randomly (or rather probabilistically according to QMâs amplitudes) becomes observable and thus the complex brains in it express consciousness.

Perhaps, someone might suggest that particles aren’t indistinguishable after all, but that would be a modification of QM, and Volos is presented as an interpretation, not as a modification.

QM entails that particles in the same quantum state are indistinguishable, and this principle is not violated by Volos. On Volos it is not the physical properties of brains which cause consciousness, but the physical properties of brains existing in an observable state of the universe.
Boltzmann brains are dealt efficiently by Volos with no modification. Indeed the Boltzmann paradox disappears â if Volos is true then you are not a Boltzmann brain. On the other hand the existence of Boltzmann brains seems to destroy the interesting property that the first naturally evolved conscious brain will appear at the earliest possible time. More about this issue in a future post.

Compare: “What Bill says is true” and “What Jane says is true” mean different things, even if Bill and Jane say the same thing

I am not sure about that.
Compare: âThe ball Bill points at is blueâ and âThe ball Jane points at is blueâ mean different things, even if Bill and Jane point to the same ball.
This doesnât sound right to me. After all both sentences make exactly the same claim, namely that a particular ball is blue. But if they make exactly the same claim then it seems to me they have exactly the same meaning. The fact that the two propositions identify the ball in different ways does not affect their meaning as far as I can see. The propositions âThe successor of 4 is a prime numberâ means the same as âThe predecessor of 6 is a prime numberâ. Nor does the fact that one sentence entails the existence of Bill whereas the other entails the existence of Jane affects their meaning. The fact that they both entail the existence of balls or even of the English language does not affect their meaning either.
Now perhaps there is an ambiguity in sentences like âWhat Bill says is trueâ. Is that a claim about Bill (namely that Bill is right in what he has just said), or a claim about what was just said (namely that what was just said by Bill is right)? Within propositional logic that ambiguity is irrelevant, because the truth value of the first meaning is identical to the truth value of the second meaning. But in oneâs experience of life the same truth value can affect oneâs worldview quite differently depending on whether one uses the sentence with the one or the other meaning. For example if Bill is a ten year old, and what he just said is the product of two 3-digit numbers he calculated in his head, then the first meaning is far more significant than the second one. Also under the first meaning there are states of affairs where one can be confident about that sentence being true even if one doesnât know what Bill has just said.
Incidentally, in some cases such ambiguities can become very significant. Take for example the famous sentence âGod existsâ. Is that a claim about God or about existence? Is it a claim about how one should understand âGodâ or about how one should understand âexistsâ?

Dianelos,
a. I don’t think it’s embarrassing, or a problem for scientific realists. Different scientists try their best, and there is no agreement. Most of them are realists. But in any case, I don’t see why any of them should feel embarrassed. If the matter is complicated and they’ve not been able to come up with a hypothesis that persuades other people, there is nothing embarrassing about it, as far as I can tell.
And if some (many) do not have an interpretation to offer beyond a realistic interpretation of the results of measurements and the like, then ‘shut up and calculate’ is a reasonable stance.
So, I don’t think there is anything embarrassing about it.
Also, scientific anti-realists have not been able to persuade the majority of scientists, either. I don’t think that the fact that competing realist interpretations do not get agreement to be any more of a problem for realism than the lack of acceptance of idealistic interpretations is a problem for idealists.
A discussion on the matter in detail would be very interesting, but it would take too long probably; as a suggestion, you might find someone a lot more qualified to discuss QM and its interpretations than I am in the “Science Discussions” forum on FRDB (a poster who goes by the name ‘Bomb#20’). While he doesn’t take a stance on any interpretation, he would probably object (if he replies) to an argument to the conclusion idealistic interpretations like the one you propose probably fare better, and might defend scientific realists from the charge of embarrassment (i.e., I can’t guarantee he’d reply, but if he does, I doubt you could find stronger counterarguments).
By the way, the same goes for the rest of the points about QM you’re making, not just a.; if you start a thread there and the thread is not moved to another subforum, you may well find an interlocutor who makes much stronger points than I do; given that you seem to have studied these matters a lot, if you’re interested in more challenging replies, you could find some over there.
b. The idea of ‘blind physical forces’ seems to suggest a lack of causation on my part. I would tend to disagree. I don’t think that explanations of a phenomena at a lower level (e.g., particles) rule out explanations at a higher level, or that causation at a lower level rules out causation at a higher level.
Regarding MWI, though, there are different ways in which it can be interpreted (no pun intended); some of them are branching universes (the most common one it seems to me), and others are already there so to speak.
In the case of universes ‘already there’, no problem (there are other problems with that idea, though); in the case of branching universes, you said earlier that each of us is a mass murderer, and that each one of us will live forever. I thought if you were talking about the branching variant, you were talking about someone who already branched away from us, and is a mass murderer.
As long as the universes split in the past, if that guy is a murderer, I’m not that guy. I’m not a murderer in any universe, even if MWI is true.
But now the question is whether each one of us will be a murderer in some universe.
Issues of identity through time are already complicated in one universe, but it’s a matter of how we classify things, in my view, and the concept of identity is not precise enough to handle the matter properly (unsurprisingly, since it didn’t develop in an environment of people who intuitively believed in branching universes or anything like that).
In any case, I would say that one of the many distinct people who would branch from me would be a mass murderer, and he would be justified in considering my present self as his past self.
c. I would say that the ‘superposition’ of Volos and the many parallel universes of MWI go by different names but they are basically parallel universes, with the twist that one of them is conscious, but the other full of zombies.
But in order to assess parsimony, let’s consider the view (leaving aside QM for now) that there is only one minds (yours), and everyone else is a zombie. Would that view be more parsimonious because it posits fewer minds?
It seems clear to me that the answer is negative. Yes, there would be fewer minds, but there would be a much greater number of kinds of entities, and further there would be little (nothing, actually) in the way of explanation as to why those different kinds of entities are physically the same, etc.
In brief, just as the view (one mind + everyone else is a zombie) is a lot less parsimonious than the normal view that humans aren’t zombies, I would say that (one universe with minds + zombie multiverse) is a lot less parsimonious than the normal MWI multiverse, as long as one can have anything ‘normal’ on MWI.
e. I don’t think that’s a difference in terms of parsimony, or at least for me, intuitive probabilistic assessment.
For instance, we may consider the view that everyone was a zombie until 1000 years ago, and then everyone became conscious as one. Then, no one experiences zombies, and that posits fewer minds, but it’s still vastly improbable.
It may be, I agree, that one may find MWI personally more distressing, but that’s another matter. Which one do I find more distressing? Tough one. I would still say that zombie multiverse is less plausible than non-zombie multiverse, which is already implausible.
f. I tend to disagree on that; in my view, our successors will probably come up with better models, which still probably won’t be exceptionless.
g. I think that that depends on what the stuff is (if they add stuff) vs. the stuff that the someone committed to the original theory has to accept (e.g., if it’s between MWI or Volos and Weinberg’s suggestion including a collapse that requires no consciousness, I find the latter much simpler).
I’m not in a position to assess how simple they are (the guy I mentioned above would be better suited), but it may well be that it’s not yet clear which one is simpler (people still trying to come up with interpretations), so I will leave it at that.
Regarding Berkeley, I will have to pass on that I’m afraid. I really don’t have time for a debate on theism, or the proper understand of our concepts about freedom; I would just say (to let you know where I’m coming from, but I’m afraid I can’t properly debate that now) that I don’t agree with the libertarian understanding of the concept, so I don’t think Berkeley would explain it. Additionally, Berkeley includes God, which in my assessment makes it much less probable than any of the other variants (my suggestion about discussing it over there some time applies to Berkeley as well, by the way).

The mechanism (or algorithm) which on Volos determines the properties of reality works as follows: At each time which is a multiple of E one (if any) of the not already âunobservableâ states of the universe in which complex brains exist becomes âobservableâ, and the complex brains in it express consciousness. All other states at this point in time as well as all states in future branches of them in the massive superposition become âunobservableâ, which means that the complex brains in them will not express consciousness (remain zombies). (As you see I tried to describe how reality is according to the Volos interpretation without using metaphorical language which one may misinterpret as entailing some kind of external or non-physical guiding hand. Volos does entail a causal connection between states in the massive superposition though.)

But that does not seem to an algorithm, or mechanism, or anything that determines what happens; rather, it seems that as a brute fact it just happens.

Thus, if B1â exists in a state of the universe which becomes âobservableâ then that brain will express consciousness. If the later B1 exists in a state which will be marked unobservable, then B1 will not express consciousness even though it is physically identical to B1â. Zombie brains are physically identical to non-zombie brains. If the later B1 exists in some branch that grows out from the state of B1â then its state will perhaps become observable and B1 too will express consciousness. State histories may contain identical brains at different points in time, and thus it is possible (though unlikely) that exactly the same consciousness will obtain at two different points in time within the unique conscious state history.

Okay, I got that, but the issue I’m trying to raise is how B1 rather than B1′, or so many others.

The point in time at which the first brain will express consciousness is deterministically fixed.Â

That does not seem to be the case, as far as I can tell based on what I read. Could you explain that, please?
For instance, let’s say that the first point in time was t0, and a brain B1.
Let B1′ be a brain physically identical to B1, at t0-E, and with almost the same evolutionary history as B1. Let BB1 a Boltzmann brain complex enough for consciousness, at t1
Â Perhaps there are several states where complex brains exist, and in this case only one of them will randomly become observable. Suppose, for example, that at the very first time tâ where complex brains evolve there are four states with such brains, namely: {B1â}, {B1â, B2â}, {B3â}, {B2â, B4â}. Only one of these states will randomly become observable.
But my question is not how the specific brain at the first state is picked.

But it does. On Volos one of those states randomly (or rather probabilistically according to QMâs amplitudes) becomes observable and thus the complex brains in it express consciousness.

There seems to be a misunderstanding. What I’m saying is that there is no probability, say, at t3 (see above), and so how does the first state is determined? Not probabilistically, since there is no probability. You say it’s deterministic, but I don’t see how that would be so.
Also, there is another issue, which is how can probabilities decide between those four states you propose, since consciousness is (causally and/or ontologically) prior to probability, so it seems that consciousness would have to happen before tagging.
But that’s another issue, not the one I’ve been trying to raise, so I’d rather leave it for later.

QM entails that particles in the same quantum state are indistinguishable, and this principle is not violated by Volos. On Volos it is not the physical properties of brains which cause consciousness, but the physical properties of brains existing in an observable state of the universe.

But the observable state is physically indistinguishable from the other one. If not, then we have the problem of whether the Earth existed 900 million years ago (or some time in the past, etc.), due to the other arguments I’ve been making.

Boltzmann brains are dealt efficiently by Volos with no modification. Indeed the Boltzmann paradox disappears â if Volos is true then you are not a Boltzmann brain.

How do I know that? I can’t even say it was more probable, as far as I can tell, that t0 and B1 are the first time and brain respectively, rather than, say, t1 and BB1. What if it was t1 and BB1?
Now, you say that the answer is that t0 and B1 are fixed deterministically. But again, I don’t see how.

Angra: you expressed lots of interesting ideas; thanks.
As for grasping a primitive concept of necessity, for me the concept arises from examples, such as this one:
(X) there can’t be contradictions that are possibly true.
Notice that ~(X) doesn’t entail a contradiction. Also, (X) isn’t entailed by the statement that whatever *is* contradictory is impossible. I don’t see a clear way to deduce that (X) is necessary on Swinburne’s account (without appealing to S5, but then how do we deduce that S5 is necessary–where the operators are defined by Swinburne’s criteria?).

Joshua,
Thank you for your reply, and your example. I have a few comments on that (I’m assuming propositions, not sentences, but let me know if you prefer to test examples involving sentences).
If you think my analysis below is mistaken, please let me know where you think it goes wrong, and maybe that will help me try to grasp the concept that you have in mind.

(X) there can’t be contradictions that are possibly true.

1. One of the first things I notice is that it sounds rather difficult to understand, in the sense that it takes some effort to try to figure out what you’re getting at, and also how it connects with the concepts of metaphysical possibility, necessity or impossibility. I’ll get to the details below, but in particular, what is apparent is that this is not the kind of example that the vast majority of people would be familiar with.
So, if the idea of metaphysical modality actually is meant to reflect some common folk concept, then people would learn it by very different kinds of examples. Even philosophers would learn it by very different kinds of examples, since they would learn it before they become philosophers â though, of course, they may develop a more sophisticated understanding later.
2. On the other hand, if the concept of metaphysical modality is not claimed to be a folk concept, then that might not be a problem, but then there is still a difficulty in using (X) as a means to learn a new concept, because examples by which one learns a concept need to be paradigmatic cases, not cases that one needs to analyze based on a previous concept, and I’m not sure why (X) would be presented as an example.
In any case, I will analyze it under the concept of metaphysical impossibility I seem to have, as follows:
3. The word ‘can’t’, in (X), seems to mean (I assess that this is the case because you’re telling me it’s one of the examples from which the concept of necessity may arise), “It is metaphysically impossible that”, so (if I understand the example correctly; please let me know if I’m not getting it right), (X) seems to mean something like:
(X’): It is metaphysically impossible that there is at least one proposition P, such that P is contradictory and P is metaphysically possibly true.
As I mentioned, that would not seem to work for me as an example of what metaphysical modality is; there seems to be nested modal claims or something like that, and assessing (X’) seems to require that I already have a concept of metaphysical modality, a way of dealing with iterated modal operators, and apparently a way of quantify over propositions.
Still, since I do have that (what I’d like to know if whether I got the wrong concept, but at least I seem to have some concept, which is the one I’ve been explaining), I will analyze (X’) under such concept.
4. (X’) has the form “It is metaphysically impossible that Q”
The way I understand the words, in order to assess whether (X’) is true, I would have to assess whether Q is contradictory, either strictly or after considering meanings, rigid designators, etc., in a sentence that expresses Q.
So, let’s assume Q:
Q: There is at least one a proposition P, such that P is contradictory and P is metaphysically possibly true.
Let P0 be one such proposition [I think that this can properly be done, by my understanding of the meaning of existential operators in this context and logic; I hope this method is uncontroversial, but if you think otherwise, please let me know, and I will formalize the choice, but it will be very long, and will take me some time].
Then, P0 is contradictory.
Then, P0 is metaphysically impossible [by my concept of ‘metaphysically impossible’, and since it’s contradictory].
Then, it is not the case that P0 is metaphysically possible [since tautologically, R is metaphysically possible iff it is not the case R is metaphysically impossible; similarly R is metaphysically impossible if and only if it is not the case that R is metaphysically possible].
Then, it is not the case that R is metaphysically possibly true (since, for any proposition R, “R is metaphysically possibly true” and “R is metaphysically possible” are equivalent, which one can properly determine using logic and the meaning of the words).
But R is metaphysically possibly true. [by assumption].
So, it is not the case that R is metaphysically possibly true, and R is metaphysically possibly true.
That is a contradiction. So, I assumed Q, and (using logic and my grasp of the meaning of words, and nothing beyond that) I obtained a contradiction.
So, it is metaphysically impossible that Q. In other words, (X’) is true. And (X) means the same as (X’). So, X is true.
5. In many cases, I may not need to consciously take all of those steps in order to assess whether a proposition is metaphysically impossible. For instance, if someone tells me that there is a person, Alice, such that Alice is a woman and it is not the case that Alice is a woman, I assess immediately that the claim is metaphysically impossible, and don’t need to consciously follow my steps in reaching that conclusion.
However, that seems to be because I internalized some concept of metaphysical possibility, and in some cases that allows me to make fast, intuitive assessments, though I can still try to assess why I come to that conclusion, and that leads me back to the criteria I mentioned.
In other, more complex cases, I require a more careful analysis. But when I do that analysis, it seems I’m doing exactly what I mentioned in my immediately previous reply to you, one application of which is my analysis of (X) (and (X’)) above.
So, upon reflection, that seems to me the way I use the expression ‘metaphysically impossible’.
As for other cases of metaphysical modality, a proposition is metaphysically possible iff it’s not metaphysically impossible, and it’s metaphysically necessary iff its negation is metaphysically impossible.

Notice that ~(X) doesn’t entail a contradiction. Also, (X) isn’t entailed by the statement that whatever *is* contradictory is impossible. I don’t see a clear way to deduce that (X) is necessary on Swinburne’s account (without appealing to S5, but then how do we deduce that S5 is necessary–where the operators are defined by Swinburne’s criteria?).

Are you referring to his criteria for sentences, or propositions (when he assumes propositions, page 18)?
The criteria for sentences would need extrapolating, and I’m not sure how his criteria for propositions works since it’s not clear to me what he might mean by “designators” in the context of propositions that are not expressible by sentences (by the way, I would like to ask whether you understand “designators” in the context of sentences or propositions).
Still, the impression I got from his paper is that the adaptation of his criteria to propositions would render something like my criteria (i.e., the criteria I proposed in my immediately previous reply to you; let’s call them “Criteria C1”, to give them a name. or some other name if you prefer), so it would work.
But if that is not the case and I misunderstood Swinburne, then I would say that criteria C1 renders (X) true, as far as I can tell, and that seems to be the one that reflects my intuitive understanding of metaphysical impossibility, as far as I can tell.
Also, C1 isn’t some criteria I propose for testing against different cases using my intuitive grasp of the term ‘metaphysically impossible’ (though of course, you, Alexander, Dianelos and/or some of the other readers may test C1 against what you/they consider to be uncontroversial cases of metaphysical impossibility), but rather, C1 seems to be the way in which I actually go about checking claims of metaphysical impossibility, by my own grasp of the meaning of the term.
6. That aside, I would like to ask how you go about checking claims of metaphysical impossibility, at least when it’s not obvious to you, but rather have to use a conscious procedure (as opposed to an intuitive unconscious one). Maybe that would help me get how our concepts differ, if they do.

Thanks Angra.
I agree with you that (Q) entails that there is a contradiction (because it entails that there is a P, such that P is both possibly true and not possibly true). Note, however, that there is a difference between a statement that reports the existence of a contradiction, on the one hand, and a statement that is or strictly entails a contradiction. I don’t believe there is a standard inference rule in first-order logic from which we can deduce the latter from (Q) (after having talked this through with a math professor).
But this may all be beside the point, anyway, because you previously suggested that a statement is necessary if we can tell that it is true a priori. And that opens up more necessary truths than I think we can get via strict logical deduction. So, in fact, our modal assessments may not come out different in most cases.
As to a procedure for “checking”, I have tools (like check for contradiction, whether it entails or precludes other things that seem necessary, predictive power, etc), but I don’t have any general procedure that I am prepared to articulate. Such are the complexities of epistemology. 🙂

Thanks, Joshua.
Regarding Q, I will give a more formal proof below, and I would suggest that you ask the math professor to check my proof if you like.
Before I begin, just a point of clarification: quantifying over propositions may have difficulties that are not present in mathematical logic. However, that is not a consideration here, since the proof can be carried out using only the tools available in mathematical logic, treating the propositions as variables (i.e., my proof does not depend on any other issue involving propositions).
I will give some definitions: (others are implicit, if needed, but the following should be clear enough; symbols like implication, etc., are used in a standard way).
a. An uppercase letter or an uppercase letter followed by a number represents a proposition.
b. MP(R): R is metaphysically possible.
c. MPT(R): R is metaphysically possibly true.
d. C(R): R is contradictory.
e. E(R)/H(R): There exists at least one proposition R such that H(R) [for instance, E(R)/MP(R) means that there exists at least one proposition R such that R is metaphysically possible].
f: A(R)/H(R): For all propositions R, H(R).
g. Rule C: It’s a rule in mathematical logic that works as a shortcut, so to speak. Essentially, it justifies going from E(R)/H(R) to H(R0). A proof of that can be found in (for instance, Mendelson, Introduction to Mathematical Logic, Chapter 2, Section 7). I will do the proof without using rule C if that is a sticking point, but that would make it considerably longer, and I really don’t see why that should be an issue (rule C is uncontroversial, and you can in any case check the proof of rule C if you like).
So, Q states:
Q: There is at least one a proposition P, such that P is contradictory and P is metaphysically possibly true.
Formalizing it:
Q: E(R)/(C(R)&MPT(R)).
The following premises can be established only by logic and using one’s intuitive grasp of the words:
P1: AR(MPT(R)âMP(R))
P2: AR(C(R)âÂ¬MP(R)).
I will now give a proof of a contradiction (I’ll say things like ‘from premises such and such’, without giving details, which would involve proofs that I think are clear, but I will give more details in later posts if needed):
P1: AR(MPT(R)âMP(R))
P2: AR(C(R)âÂ¬MP(R)).
Q: E(R)/(C(R)&MPT(R)).
1. C(P0)&MPT(P0) [from Q, applying rule C].
2. C(P0) [from 1].
3. C(P0)âÂ¬MP(P0) [from P2].
4. Â¬MP(P0) [from 2. and 3.]
5. MPT(P0) [from 1.]
6. AR(MPT(R)âMP(R)) [from premise P1].
7. MPT(P0)âMP(P0). [from 6.]
8. MP(P0) [from 5. and 7.]
9. MP(P0)&(Â¬MP(P0)). [from 8. and 4.] That is already a contradiction. While this suffices, we may also set aside any reference to the specific P0 and obtain a generic contradiction, as follows:
10: A(R)((R&(Â¬R))â(A(Y)(Y&Â¬Y))) [theorem; basically, a contradiction entails everything]
11. MP(P0)&(Â¬MP(P0))â(A(Y)(Y&Â¬Y)). [from 10].
12. A(Y)(Y&Â¬Y). [from 9. and 11.]
13. (Y&Â¬Y). [from 12]
So, I conclude that C1 (i.e., the criteria I suggested) does yield that (X’) (and hence X) is true, since I derived a contradiction from Q, using only logic and my intuitive grasp of some terms.

But this may all be beside the point, anyway, because you previously suggested that a statement is necessary if we can tell that it is true a priori. And that opens up more necessary truths than I think we can get via strict logical deduction. So, in fact, our modal assessments may not come out different in most cases.

I agree that our modal assessments may not come out different in most cases (side note: I understand ‘most cases’ as counting cases we might realistically encountered; one case of disagreement might be extended to infinitely many similar ones, but that’s not the issue).
At least, so far we both seem to agree on all of the cases considered by most to be non-controversial, and there are plenty of those.
That said, and regarding of what I suggested earlier, some clarification might be needed.
I said earlier “So, in short, it’s something we can tell a priori by means of our linguistic competence and logic (“a priori'” is not beforeÂ everything, of course; we need to learn the words before that).Â “, and made some similar statements.
In that context, the ‘a priori’ was qualified by the reference to linguistic competence and logic.
For instance, arguably, I can tell a priori that I exists [though that’s debatable; one would need to qualify the ‘a priori’ more specifically], but that’s not a necessary. In any case, the ‘a priori’ was meant to be qualified by the means of making the a priori assessment, namely logic and our linguistic competence.

As to a procedure for “checking”, I have tools (like check for contradiction, whether it entails or precludes other things that seem necessary, predictive power, etc), but I don’t have any general procedure that I am prepared to articulate. Such are the complexities of epistemology. 🙂

Okay, thanks.
The first tool is covered by C1. The second one seems to be so as well, since C1 may be used to check for other necessities, and my criteria does entail that a proposition that entails the negation of a necessary proposition is impossible.
So, in order to assess whether there are differences between your concept of metaphysical impossibility (and then possibility, etc.) and what seems to be my concept, I would like to ask if you have one tool that you find incompatible with C1 (e.g., if it would yield some proposition necessary while C1 says it’s not).
Still, I realize that that might be difficult to find as well, so if you have any alternative suggestions as to how to assess whether our respective concepts of metaphysical modality are the same, or how I might be able to learn the concept you’re using, that might help.
In particular, if there are some cases in which you immediately and clearly find that some proposition is impossible but I find them possible, that might be a good start (alternative suggestions are welcome, of course :)).

Angra,
To say in a philosophical context that âmost scientists are realistsâ can be misleading. A fact about the human condition is that we find it easier to think mathematically when we visualize worlds patterned on our experience of the physical objects around us, to think about causality in mechanistic terms, etc. Thus itâs quite natural that scientists should do the same, and even if scientific realism is false such epistemic customs do not appear to affect their productivity, as evidenced by the fact that they have productively used and greatly advanced QM without really knowing and mostly without really caring about its metaphysical implications. The âshut up and calculateâ dictum does not mean âdonât visualize anything when you do the calculationsâ but âcalculate without caring whether what you visualize makes any senseâ. Finally, scientists (and, not surprisingly, especially great scientists) tend to be very philosophically uninformed â so even though the deliverances of science are of philosophical interest, I donât think that scientistsâ opinions in matters philosophical carry special weight.
The problem at hand is clear: To describe a reality that would produce the phenomena QM describes and which satisfies the intuitions of the scientific realist. And I think that when one observes that the scientists who have actually worked on this problem have really nothing to show after 80 years of effort except increasingly implausible suggestions and increasingly diverse opinions – then this says something. Perhaps more philosophers should work on this problem. Itâs not really a matter of mastering the math of QM â the problem can be stated using just a few observational facts as well as the general features of QM.

I don’t think that explanations of a phenomena at a lower level (e.g., particles) rule out explanations at a higher level, or that causation at a lower level rules out causation at a higher level.

Depends on what one means by âexplanationâ. If one thinks that explanations are patterns present in data (as all scientific explanations apparently are), then explanations can exist at any level with no recourse to what lies bellow or above. On the other hand to my knowledge there is not one example of top-down causation, as evidenced by the fact that one can always (at least in principle) simulate the high level events using only low level causation.

But in order to assess parsimony, let’s consider the view (leaving aside QM for now) that there is only one minds (yours), and everyone else is a zombie. Would that view be more parsimonious because it posits fewer minds?

I think solipsism is a more parsimonious view, and I donât see how it posits a greater number of kinds of entities. In any case parsimony by itself is not what we are after. Occamâs razor says that we shouldnât multiply entities unnecessarily. And in the context of our discussion the multiplication of minds to the humungous degree that the MWI entails is not only unnecessary but also produces many absurd implications.

Additionally, Berkeley includes God, which in my assessment makes it much less probable than any of the other variants

I understand, but this does not affect my claim that there are unproblematic ontological interpretations of QM, and that only the conjunction of scientific realism and QM is found to be problematic. My argument is only that the discovery and great success of QM lowers the probability of scientific realism being true. (And, I understand, most theists are scientific realists also.)

But that does not seem to an algorithm, or mechanism, or anything that determines what happens; rather, it seems that as a brute fact it just happens.

Right, the Volos interpretation is an indeterministic metaphysics. As is ontological Copenhagen. As is any epistemic interpretation of QM.

[That the point in time at which the first brain will express consciousness is deterministically fixed] does not seem to be the case.

The massive superposition of state histories of the universe (the universeâs wavefunction) is deterministic. And we agree that there is a particular property of physical systems which expresses consciousness â and which property, as we have been saying here, characterizes the âcomplex brainâ. Now imagine the universeâs wavefunction as a tree of ever branching state histories, and a horizontal line representing the point in time slowly advancing upwards. At some point and for the first time a state of the universe will be encountered in which a complex brain obtains. Here the Volos algorithm picks this state for consciousness (or randomly picks one, in the case that there are more than one states with complex brains in them), and marks all other states and their branching futures as unobservable. Since the massive superposition is deterministically fixed so is also the point in time when the first complex brain will be encountered, i.e. the time when for the first time conscious experience obtains. Iâll leave the issue of Boltzmann brains for last.

What I meant is this: The state of reality, i.e. all the states of the universe at the same point in time in the massive superposition, is fixed before the first complex brain at t0. But it becomes indeterministic after t0, because now at each point in time only one state contains conscious complex brains, and which that state will be depends on an indeterministic process. Thus before t0 it makes no sense to speak of probabilities (in the sense of counterfactuals) for nothing different is possible. But even before t0 one can speak of frequencies, i.e. about in what proportion of states a particular property obtains.

But the observable state is physically indistinguishable from the other one.

On Volos, the only observable state history is our own (whether we happen to be the first conscious biological organisms or not), and in that state history the Earth does exist for some 4.5 billion years. In many other unobservable (i.e. without consciousness) state histories the Earth also exists for 4.5 billion years. In most unobservable state histories the Earth doesnât exist at all.

Dianelos,
I’m not sure in which sense you say that saying that most scientists are realists can be misleading, but I was actually agreeing with what you said in an earlier post, when you said that most physical scientists are scientific realists.
Regarding the fact that most scientists are not philosophically informed, I agree, but then I don’t think that’s a problem, and I don’t think that questions of whether there is a multiverse, etc., are not within the scope of science (if that’s what you’re suggesting; else, I’m not sure about your point).
As for “shut up and calculate”, I’m not sure what part of my post you’re objecting to: the point I was trying to make was that taking an instrumentalist position was reasonable if one does not have an interpretation beyond a realistic interpretation of the fact that we make measurements, etc.
I wasn’t suggesting that the expression meant âdonât visualize anything when you do the calculationsâ.

The problem at hand is clear: To describe a reality that would produce the phenomena QM describes and which satisfies the intuitions of the scientific realist. And I think that when one observes that the scientists who have actually worked on this problem have really nothing to show after 80 years of effort except increasingly implausible suggestions and increasingly diverse opinions – then this says something. Perhaps more philosophers should work on this problem.

Perhaps. Or perhaps no present-day primate can make sense of it in any way that appeals to her pretheoretical intuitions about the world. But perhaps that’s not the case. In any event, since QM is not a complete picture of reality, maybe when a more complete one is available, things will get better. Or maybe they will get even worse. I don’t know, so take no stance.

Â On the other hand to my knowledge there is not one example of top-down causation, as evidenced by the fact that one can always (at least in principle) simulate the high level events using only low level causation.

I get the impression we probably have a very different view on the meaning of ’causes’.
For instance, even if one can always simulate a bullet shot using particles, I don’t think that that is a problem for statements like “The fall injured him, but what caused his death was a GSW to the heart.”

I think solipsism is a more parsimonious view, and I donât see how it posits a greater number of kinds of entities.Â

I posits conscious arrangements of particles and unconscious identical arrangements of particles. That indicates some other stuff, like a soul…unless it the claim that they’re identical is removed and then you have different types of particles.
At any rate, it posits more kinds of events (like physically identical events with different properties with regard to consciousness).

Â In any case parsimony by itself is not what we are after. Occamâs razor says that we shouldnât multiply entities unnecessarily. And in the context of our discussion the multiplication of minds to the humungous degree that the MWI entails is not only unnecessary but also produces many absurd implications.

But the question is when it’s “unnecessarily”: the only way Occam’s razor would be true would be if it’s unnecessary whenever positing more entities would make the theory less probable (that’s epistemic probability), so in the end it’s a matter of probabilistic assessments.
The theory that the world is 200 years old posits surely fewer entities, but that would be far less probable.

I understand, but this does not affect my claim that there are unproblematic ontological interpretations of QM, and that only the conjunction of scientific realism and QM is found to be problematic.Â

It does in the sense that I disagree with your claim, if the interpretation you deem unproblematic is one that contains God.

My argument is only that the discovery and great success of QM lowers the probability of scientific realism being true. (And, I understand, most theists are scientific realists also.)

Okay, and I don’t agree, for the reasons I’ve explained.

Right, the Volos interpretation is an indeterministic metaphysics. As is ontological Copenhagen. As is any epistemic interpretation of QM.

Okay, but I was taking issue with the claim that “The mechanism (or algorithm) which on Volos determines the properties of reality works as follows:”. I was saying that that was not an algorithm.
Regarding epistemic interpretations, they don’t seem to posit indeterministic metaphysics, even if they do not offer an algorithm.

The massive superposition of state histories of the universe (the universeâs wavefunction) is deterministic. And we agree that there is a particular property of physical systems which expresses consciousness â and which property, as we have been saying here, characterizes the âcomplex brainâ. Now imagine the universeâs wavefunction as a tree of ever branching state histories, and a horizontal line representing the point in time slowly advancing upwards. At some point and for the first time a state of the universe will be encountered in which a complex brain obtains. Here the Volos algorithm picks this state for consciousness (or randomly picks one, in the case that there are more than one states with complex brains in them), and marks all other states and their branching futures as unobservable. Since the massive superposition is deterministically fixed so is also the point in time when the first complex brain will be encountered, i.e. the time when for the first time conscious experience obtains. Iâll leave the issue of Boltzmann brains for last.

Two points:
1. Then it seems the first such state contains one or more Boltzmann brains, not evolved brains.
2. If the first state contains one or more Boltzmann brains, that would require probabilistically picking before consciousness.
Okay, granted, you said you’ll leave the issue of Boltzmann brains for later. But the point is that the issue is central, since your description of Volos seems to entail that a Boltzmann brain will be the first conscious entity, but you say it’s an evolved brain.

But even before t0 one can speak of frequencies, i.e. about in what proportion of states a particular property obtains.

But that doesn’t seem to work as far as I can tell, because regardless of frequencies, the Volos interpretation is requiring a probabilistic choice before consciousness. Unless you posit two kinds of probabilistic choices, one before consciousness, and one after consciousness, but that further complicates the problem.
Side note: an additional problem is that Volos doesn’t tell us anything about the other probability, other than the fact that the first complex brain (no matter how infrequent it is in the superposition) is going to be picked if there is one, or one of them will be picked (again, regardless of how infrequent they are) if there is more than one.

On Volos, the only observable state history is our own (whether we happen to be the first conscious biological organisms or not), and in that state history the Earth does exist for some 4.5 billion years. In many other unobservable (i.e. without consciousness) state histories the Earth also exists for 4.5 billion years. In most unobservable state histories the Earth doesnât exist at all.Â

Okay, I get that. I’m not sure what part of my post you’re objecting to here. Could you clarify, please?

Angra,
On the issue of Boltzmann brains: Boltzmann brains obtain when physical particles spontaneously arrange themselves into a âcomplexâ brain in some part of space and maintain their order long enough for consciousness to obtain. In the general case I am here discussing, Boltzmann brains donât have to look like human brains at all, they only have to realize the consciousness expressing physical property for a fraction of a second.
Now Boltzmann brains are permitted by QM, and therefore in all ontological interpretations of QM where the universeâs wavefunction is real (such as the MWI, the MMI, and Volos) Boltzmann brains do obtain as real objects. And as you say they obtain very early, probably no later than a million years after the Bing Bang, whereas naturally evolved brains need billions of years more (since they require Goldilocks planets, biological evolution, etc). So letâs see how Volos deals with Boltzmann brains.
The Volos algorithm does not distinguish between complex brains spontaneously produced by quantum effects and complex brains produced by natural evolution. So when the first primitive Boltzmann brain is encountered at t=tb consciousness is realized in one âobservableâ state, and all other states and their branching future histories become âunobservableâ. Letâs now consider the next relevant point in time t=tb+E (with E being the smallest time interval in which changes in conscious states obtain, approx. 1/10 segs.) The one physical state of the universe at tb with the conscious Boltzmann brain in it will have branched into a huge number of successor physical states. Boltzmann brains are highly unstable, so in almost all of the successor states no Boltzmann brains will exist, but in a small fraction 1/B a Boltzmann brain will exist. (B is a very large number, I suppose something like 10^(10^1000). ) Further in 1/(B *B) of the states two Boltzmann brains will exist. Even more rarely, i.e. in less than 1/(B*B) of the successor states, a significantly more complex Boltzmann brain will exist. Given these relative frequencies of states with complex brains, the state which at tb+E will become observable (i.e. consciousness including) will almost certainly be one where exactly one primitive Boltzmann brain exists. The same story repeats itself at tb+2E, and so on. For a long time then the conscious state history of reality will be of just one Boltzmann brain existing in the âobservableâ universe and having some extremely primitive and discontinuous (without any memories) conscious experience.
Meanwhile in the physical state history of the observable universe stars form, supernovaâs produce heavy elements, other stars with heavy planets appear, on Goldilocks planets life starts to evolve, and at some time t=t0 several billions years later the first biologically evolved complex brain for the first time obtains. So at t0 there are states with Boltzmann brains but also with biological complex brains. Which state is indeterministically picked by Volos at t0 to be observable (i.e. consciousness including) is not particularly relevant. To simplify the discussion letâs suppose that at t0 a state is picked where both a biological brain and a Boltzmann brain exist. What happens at t=t0+E? Given the physical stability or persistence of biological brains virtually all states at t0+E will contain that same biological brain and in a significant proportion they will still be complex (consciousness expressing) ones. But only 1/B of the states at t0+E will contain a Boltzmann brain. Thus at t0+E almost certainly a state will be picked where only biological brains exist. And so on in the future. From now on the state history of the observable universe will contain no Boltzmann brains, but only biological brains experiencing their physical environment.
So, in conclusion, there are two epochs in Volosâs conscious state history: Between tb and t0 with just one Boltzmann brain having a very primitive conscious experience, and after t0 with a growing number of biological brains having an increasingly complex conscious experience. Thus on Volos the so-called Boltzmann paradox disappears, since Boltzmann brains of the complexity required for human-like experience will (almost certainly) never obtain within the observable universeâs state history. If Volos is true then we are not Boltzmann brains.
Now the advantage of a biological brain over a Boltzmann brain lies of course with its physical persistence into most of the observable universeâs state successors. So what about Boltzmann planets (or, more precisely, Boltzmann planetary systems)? These too are spontaneously produced but are also physically stable. Boltzmann planets obtain quite early in the massive superposition, probably only a little later than tb. But given the Volos mechanics such states will (almost certainly) never obtain in the state history of the observable universe.
Not so on MWI. Here Boltzmann planets with conscious and intelligent life on them are real (and not zombies as on Volos). On MWI by far most civilizations grow on Boltzmann planets. Which planets, incidentally, except for extremely rare exceptions look very different from ours, for they donât appear to have any geological or evolutionary history, but appear to have sprung ready-made out of nothing – as indeed in a sense they have. Thus on MWI the proportion of natural or apparently planets with conscious life on them is extremely small. If MWI is true then we are extraordinarily lucky to have what appears to be a natural planet as a habitat. Thus, as far as I can see, the evidence from the geological and biological past we see around us falsifies the MWI hypothesis.
Letâs now discuss Boltzmann organisms. These are the simplest physical structures which Darwinian evolution can work with, i.e. the simplest life forms. Since they are much simpler than Boltzmann brains (and of course much simpler still than Boltzmann planets) they obtain much more frequently in the massive superposition. (Fred Hoyle has estimated their B at 10^40000.) Consider now the earliest states of the universe with Goldilocks planets in them. In some of these states Boltzmann organisms will obtain on such planets, they will be physically stable, and natural evolution will quickly start there. A few billion years later the first complex biological brain will evolve (and on Volos will become conscious in the single observable universe that exists). Some time later intelligent scientists will study their environment with its many signs of geological and biological history, will discover natural evolution, and will also discover that the earliest life forms started very early on their planet. Before their discovery of QM (or perhaps before thinking about Boltzmann organisms) they will wonder about the mechanisms that gave rise to life and especially so readily, and speak about the problem of the origin of life. Which is exactly what we find to be the case in our world.
So here we have a successful retrodiction of Volos. Indeed, the Earth formed about 4.5 billion years ago as a fiery sphere, the first stones on its still very hot and unstable surface appeared after half a billion years, and after only another half a billion years there was already life here (within an environment we would today call hellish). If it turns out that no natural mechanisms beside spontaneous Boltzmann organisms can explain the origin of life so early on our planet, we shall have reason to believe both that life on Earth started with a Boltzmann organism and that Volos is the only interpretation of QM that fits the large scale data and satisfies the scientific realistâs intuitions. (Boltzmann organisms do not explain the early origin of life on MWI or MMI. Consider all state histories in the massive superposition where there is Earth with life on it. Compared to the number of state histories where life starts 1 billion years after its formation (as in our actual case), there are many more state histories where life starts at 2 billion years, and still many more where it starts at 3 billion years. Thus most Earth scientists in the massive superposition observe a very late origin of life. But perhaps ontological Copenhagen can explain the early origin of life too.)

Now Boltzmann brains are permitted by QM, and therefore in all ontological interpretations of QM where the universeâs wavefunction is real (such as the MWI, the MMI, and Volos) Boltzmann brains do obtain as real objects.Â

In usual collapse interpretations â not Volos, in which ‘collapse’ is merely tagging -, I’d say those objects do not exist until collapse happens. But that’s not the main issue at this point, so I’ll leave it at that.

The Volos algorithm does not distinguish between complex brains spontaneously produced by quantum effects and complex brains produced by natural evolution. So when the first primitive Boltzmann brain is encountered at t=tb consciousness is realized in one âobservableâ state, and all other states and their branching future histories become âunobservableâ. Letâs now consider the next relevant point in time t=tb+E (with E being the smallest time interval in which changes in conscious states obtain, approx. 1/10 segs.)Â

I don’t know why E would have to be so long. For now, I’ll grant that it’s E for the sake of the argument. but I have a couple of questions:
a. Why can’t conscious states change more quickly, perhaps depending on the specific type of brain, with fast-changing brains and slow-changing brains? Or is E brain-independent? If it’s brain-independent, how do we know what’s E? (i.e., is it a condition in Volos, apart from QM?).
b. Do changes in physical states occur without corresponding changes in conscious states?
In other words, is it possible that the physical state of a brain changes while the conscious state remains the same? (either answer might be problematic, but I’ll leave that for later).

The one physical state of the universe at tb with the conscious Boltzmann brain in it will have branched into a huge number of successor physical states. Boltzmann brains are highly unstable, so in almost all of the successor states no Boltzmann brains will exist, but in a small fraction 1/B a Boltzmann brain will exist. (B is a very large number, I suppose something like 10^(10^1000). ) Further in 1/(B *B) of the states two Boltzmann brains will exist. Even more rarely, i.e. in less than 1/(B*B) of the successor states, a significantly more complex Boltzmann brain will exist. Given these relative frequencies of states with complex brains, the state which at tb+E will become observable (i.e. consciousness including) will almost certainly be one where exactly one primitive Boltzmann brain exists.

1. That seems to depend on the size of the universe. Still, for now, I’ll assume for the sake of the argument that that is so, but I have a questions here as well: Are you ruling out an infinite universe?
2. In any case, this goes against a probabilistic understanding of QM, which says that the probability of Boltzmann brains is incredible small.
In other words, on this account, it seems the probability that there will be a Boltzmann brain at tb+E is, according to a probabilistic interpretation of QM, no more than 1/B, but on Volos, the probability that a Boltzmann brain will exist at tb+E is 1.
Indeed, assuming Volos, we get with probability 1 a conscious Boltzmann brain at tb, one at tb+E, etc.
So, assuming Volos, we would need to separate two probabilities: the correct probability given by Volos, and the fake probability given by QM, which are vastly different.
3. Moreover, the change also continues after the Boltzmann brain phase, since all physical states not containing brains complex enough for consciousness are ruled out and so have probability zero, even though according to a probabilistic interpretation of QM, they have very low, non-zero probability, so the change remains later, even if its effects are smaller.
While I believe there probably are improvements to be made to QM, I would say it’s a very good approximation, and Volos introduces very significant changes to it, without any good evidence to back it up. On the other hand, other corrections seem to include lesser changes, also do not add ontological complexity by positing the possibility of physically identical states which are different with respect to consciousness, and also do not need to posit zillions of Boltzmann brains in the past.
There are other issues, but I’ll leave it at that for now.

Sorry, there is a mistake in my immediately previous post. A probabilistic interpretation does not need to give the state with Boltzmann brains at tb+E at most 1/B (if I’m reading the interpretation you’re describing properly).
But in any case, the point remains that, for billions of years since the first Boltzmann brain, enormously improbable (by probabilistic QM) states continue to obtain, whereas on Volos, one should give probability 1 to states with Boltzmann brains, at any time between tb and t0 (since one of such states certainly obtains).

Hi Angra,
Cool proof.
I’d say your premise P1 is an example of a necessary truth whose necessity I am unable to discern using the criteria of contradiction. In fact, the premise is controversial (and debated) among truth theorists.
Rule C might be another example. (I’d have to investigate it further: I didn’t see a proof *of* rule C in the section you referred to, though I checked using google books, and there was a page missing.)
At any rate, my hunch is that you pack a lot into C1 using ‘can tell a priori’, in which case P1 and rule C come out true (and it’s hard for me to distinguish your criteria from mine)

I’d say your premise P1 is an example of a necessary truth whose necessity I am unable to discern using the criteria of contradiction. In fact, the premise is controversial (and debated) among truth theorists.

Okay, I’ll explain how I derive P1, and consider a couple of objections.
P1: AR(MPT(R)âMP(R))Â
P1 states that for every proposition R, R is metaphysically possible true if and only if R is metaphysically possible. It’s clear that P1 is equivalent to the conjunction of two other premises:
P1.1: AR(MP(R)âMPT(R))Â
P1.2.: AR(MPT(R)âMP(R)).
(In my earlier proof, I would only need P1.2.; I’ll come back to this point later)
a. Let’s assume that P1.1 is not true. That entails there is a proposition, say R0, such that R0 is metaphysically possible, but it’s not metaphysically possible true.
So, let R1 be the proposition That R0 is true. Then, R1 is metaphysically impossible.
On my understanding on the terms in question, then R1 entails a contradiction, after considering the meaning of the words, including rigid designators and their referents. But then, so does R0, since R0 and R1 are equivalent.
But that contradicts the assumption that R0 is logically possible.
b. Let’s assume that P 1.2. is not true. Then, reasoning essentially just as above, I derive a contradiction.
So, I conclude that P1 is true.
Two objections can be raised to this:
Objection i. Maybe R0 and R1 are not equivalent.
In order to show equivalence, I need to show the following:
P3: A(R): (RâThat R is true).
P4: A(R): (That R is trueâR).
Let’s say that P3 is false. Then, we have (for some R2; I might have used R0 and R1 directly).
R2 and it is not the case that R2 is true.
But that’s contradictory, as far as I can tell, and as I understand the words.
Similarly, P4 is true, and then R0 and R1 are equivalent.
Someone might still object to that and say that my understanding of the words is mistaken, and that it’s not a contradiction to say R2, and it’s not the case that R2 is true, for some proposition R2.
I would disagree with such claim, again, using my own intuitive grasp of the term ‘proposition’.
However, if I were to assume for the sake of the argument that my grasp of the term ‘proposition’ is erroneous to the point of being mistaken about that, then under that assumption, I would withdraw my assent to (X) or (X’), given that under that assumption, I would assess that I do not understand the word ‘proposition’ nearly enough to make that kind of assessment about propositions.
I would perhaps also withdraw my conditions for metaphysical necessity when it comes to propositions, and make no claims about metaphysical necessity, other than, perhaps say that propositions that can be expressed by sentences that are contradictory regardless of the meaning of the words (i.e., by their form alone) are metaphysically impossible.
So, in brief, I think that objection i fails for the reasons I argued above, but if I assume it works, then I withdraw assent to (X).
Objection ii: What if the proposition R0 is not expressed in any language at all, and further, there are no words, meaning of the words, rigid designators, etc., in any language (human or not), when it comes to R0? In that case, then maybe R0 is metaphysically possible, and That R0 is true is metaphysically impossible, and rule C1 (i.e., the criteria I gave for metaphysical impossibility) does not apply.
Let’s call propositions such that there are no words, meaning of words, etc., ‘propositions of type T’, to give them a name.
I have to admit that I’m not sure I understand what it would mean for a proposition to be of type T, but in that case, given that there are no words, meanings of words, etc., then a proposition like that would be contradictory after considering the meaning of words, etc., iff it’s contradictory before considering them (since there is nothing to consider in the first place).
But if so, then applying that to R0, and R1 above, we get that R0 is not contradictory, but it’s contradictory to assert that R0 is true. But that’s a contradiction, again by the meaning of the words, and just as in the analysis given above, in reply to objection i. If that analysis fails, then my reply would be as in the reply above under the assumption that my reply to objection i fails.
On the other hand, someone might say that a proposition may be in category T and not be contradictory, yet be metaphysically impossible. But if that is the case, then I do not know then what they mean by ‘metaphysically impossible’, in which case it’s true that my analysis of the concept fails. Under that assumption, also I would not take a stance on whether (X) is true.
That said, I would like to ask you a couple of questions:
1. You say you’re unable to discern whether P1 is true by means of the criteria of contradiction, and by that you mean, if I read you correctly, the criteria I proposed earlier, i.e., criteria C1. I explained above how I would derive P1 using said criteria. I would like to ask you what part of the argument you don’t accept.
2. How would you go about trying to assess whether P1 is true?
I’m not asking for a detailed procedure, but it’d like to know how you’d approach the matter, to look for similarities and dissimilarities in our respective criteria.

Rule C might be another example. (I’d have to investigate it further: I didn’t see a proof *of* rule C in the section you referred to, though I checked using google books, and there was a page missing.)

Strictly speaking (and I see I may not have been clear enough) rule C is a rule for carrying out proofs, rather than a theorem, or metatheorem.
What is a metatheorem with respect to a first-order system is that if there is a proof of a formula (from some axioms) using rule C, there is a proof of the same formula without using rule C.
The proof actually gives an algorithm for that.
So, I can modify my proof above and give a proof that does not use rule C. However, I guess your question might be whether criteria C1 (i.e., the criteria I offered for metaphysical impossibility) allows one to establish that the following is necessary:
PR(C): If there is a proof of a formula (from some axioms) using rule C, there is a proof of the same formula without using rule C.
To say that PR(C) is false would be to equivalent to saying that that there is some formula that derived from some first-order axioms using rule C, such that there is no proof of that formula that does not use rule C.
That seems to be a claim, as I understand the words, that there is some specific formula like that, but then assuming that there is such specific formula, then a contradiction can be derived by applying the algorithm and deriving the formula from the axioms without using rule C.
Now, you might argue that I already used rule C, in order to derive the contradiction. But I didn’t assume PR(C) specifically, and the choice I made is based on my intuitive grasp of the terms (in particular, claims like ‘there is’, etc.).
However, if I’m mistaken about that, and given that I generally do use that rule in order to derive contradictions whenever checking for metaphysical impossibility, then my conclusion would be that that mistake also led to a parallel mistake when I proposed criteria C1 as reflecting my thought processes when considering metaphysical impossibility, since (under this assumption) I should have included the choice as a means of deriving the contradiction in addition to the ‘meaning of the words’ condition (instead of considering it included). A problem with this variant is that I don’t think that’s the case (I do think it’s included).
But still, if you disagree, I would then offer a second account that explicitly includes that, and which seems to reflect the way I go about checking metaphysical impossibility:
So, criteria C1 for checking whether P is metaphysically impossible consists in checking whether P entails a contradiction under the following conditions:
i. The meaning of the terms in P, including the referents of rigid designators, are accounted for.
ii. If P states ‘There is an X such that X has property F’ (for some X, F), then one may assume F(X0) in order to derive a contradiction from P.

At any rate, my hunch is that you pack a lot into C1 using ‘can tell a priori’, in which case P1 and rule C come out true (and it’s hard for me to distinguish your criteria from mine)

My hunch would be that you’re packing too little. 😉
So, I partially agree with your point above, in the sense that I think that that probably explains much of our disagreement on C1.
However, there are other cases in which I’m not sure our respective criteria are similar (e.g., in some cases when causation is involved, etc.).

Joshua,
Regarding your question about rule C (or about PR(C)) above, this seems to be a specific case of a more general situation, namely meta-theorems of first-order logic.
As I see it, denying meta-theorems does involve a contradiction by C1 and so in particular, there was no need to include condition ii.
On the other hand, if you think denying meta-theorems does not always entail a contradiction based on C1, then adding the conditions ii. in C1′ might be insufficient…I’m not sure what the reason for the disagreement is, though…. perhaps, it’s a disagreement about what counts as ‘meaning of the terms’.

Hi Angra,
Maybe an easier example would be the inference rules themselves. They are assumed *in order to* deduce contradictions, etc. But their necessity is grasped (and not just because they are deducible by those very rules!). (Also, even if your proof goes through, I’d say we grasp the impossibility of the claim prior to grasping the deduction of a contradiction from it.)
In your proof, you say that “R2 and it is not the case that R2 is true” is contradictory. I don’t see how to deduce a contradiction just from the meaning of the words. In fact, I use this as a premise in an argument for abstract propositions, and I take it to be the most controversial of my premises. How do I motivate the premise? Well, I *try* to argue that it makes the best sense of an ontology in which there are true things (and I presuppose that ontology for my audience). Anyway, your overall proof may not need this, as you point out. As for rule C, if there is a way to give the deduction without that rule (and maybe there is), I’d like to see it. (Perhaps a simpler experiment would be to deduce a contradiction from “there are true contradictions”.)
I don’t have a general criteria to apply in every case. From my understanding, discerning the necessary and the possible is like discerning the true and the false: there is no general procedure to deduce every case.

Joshua,
Regarding the rules, I’d ask for a bit more precision. Y
You mean something like:
RU1: For any propositions P and Q, (PâQ) and P entail Q.
If the claim is that metaphysically necessarily RU1 is true, then it’s true I don’t need to derive a contradiction. As I mentioned before, sometimes one can do that immediately.
In this case, I’d say that RU1 is clearly strictly logically necessary, and I know strict logical necessity entails metaphysical necessity (and I don’t know for sure how I originally figured that out).
On the other hand, when it comes to metaphysical impossibility, it seems to me that I do check for contradictions, as explained in my proposed definition, though that too can be done indirectly (e.g., if I already know that P is metaphysically necessary, I don’t need to check for contradictions to tell that Â¬P is metaphysically impossible, since I also know that if R is metaphysically necessary, then Â¬R is metaphysically impossible).
So, intuitively, we use different procedures; a question is which one is the most basic one (or even if there is one)?
At least, when it comes to metaphysical impossibilities, the rule I offered seems to reflect the way I go about it. How about metaphysical necessities?
It might be that the basic procedure is not a reverse of the procedure for checking for metaphysical impossibility, though it’s equivalent (i.e., maybe we would intuitively go about checking metaphysical possibility of P and metaphysical impossibility of Â¬P in different ways; it’s kind of weird in a sense, but then human psychology sometimes is).
That would require coming up with another procedure (other than criteria C1) to check for metaphysical necessity, and use C1 for metaphysical impossibility, though given that P is metaphysically necessary iff Â¬P is metaphysically impossible (which we figured out somehow), the two would be equivalent.

In your proof, you say that “R2 and it is not the case that R2 is true” is contradictory. I don’t see how to deduce a contradiction just from the meaning of the words. In fact, I use this as a premise in an argument for abstract propositions, and I take it to be the most controversial of my premises

I have to admit I have difficulty with this.
R2 entails (as I understand the words) the proposition that R2 is true, and that contradicts the claim that it’s not the case that R2 is true. For instance, if R2 says that the cat is on the mat.
P: The cat is on the mat.
C: It is true that the cat is on the mat.
If that’s controversial when it comes to propositions (in the sense that some philosophers object), then I would say I disagree with those who object. For that matter, there are philosophers who object to (Â¬Â¬PâP), but that seems obvious to me as well, and I think that those denying it are not using the words properly in that particular instance, perhaps due to some belief in a philosophical theory that posits otherwise.
That said, I may grant for the sake of the argument that I don’t know whether the proposition above (i.e., R2 and it is not the case that R2 is true) entails a contradiction, considering the meaning of ‘proposition’ and the other words (it seems obvious to me it does).
Then, under that assumption (say, assumption A1):
a. I withdraw my assent to (X’), and to (X), because under that assumption, I’m not confident that I know the meaning of the words in (X) and (X’) enough to any assessments (so, I don’t deny (X), either).
b. I withdraw many other claims about propositions (and would stop believing them, if I actually came to believe A1), since I reckon my grasp of the meaning of the term ‘proposition’ is too shaky (i.e., more precisely, too different from the actual meaning) to be confident in that I can properly make such claims.
c. In particular, I would also withdraw my proposed criteria C1, in a sense: I would say that it still captures my intuitive grasp of what it means for a proposition to be metaphysically impossible, but it turns out that that intuitive grasp is not good enough to make reliable assessments about metaphysical impossibility of propositions.
d. A number of other things that I would need a lot more time to think about. The implication of assumption A1 don’t go as far as, say, those of rejecting (Â¬Â¬PâP) since, luckily, it’s limited to propositions, but when it comes to propositions, it does seem to have wide-ranging effects; I would probably ask “What do you mean by ‘proposition’?”, and try to avoid talk in terms of propositions.

How do I motivate the premise? Well, I *try* to argue that it makes the best sense of an ontology in which there are true things (and I presuppose that ontology for my audience).Â

I wouldn’t include that in an ontology; I’m not sure, but there might be a difference in the way we’re using ‘entity’.

Anyway, your overall proof may not need this, as you point out. As for rule C, if there is a way to give the deduction without that rule (and maybe there is), I’d like to see it. (Perhaps a simpler experiment would be to deduce a contradiction from “there are true contradictions”.)

a. If by ‘overall proof’ you mean the proof of (X’) (and thus of (X), since at least those two are equivalent) – if not, please clarify -, then:
a.1. It does not require rule C, since everything that provable by rule C in a first order language is provable without it, and (X’) can be formalized in first-order language, as I did in my proof (the proof only requires to deal with a few some properties of propositions, so propositions can be treated as variables in this context, as I did). However, the algorithm for eliminating rule C (the one I know) uses another metatheorem (i.e., Deduction Theorem). Of course, there is also an algorithm for eliminating the use of the Deduction Theorem, so combining the two I have an algorithm for eliminating the use of Rule C without using another metatheorem. But it’s generally long (I don’t know how long it would be in this particular case; I’d have to apply the algorithm), so I’ll need time for that.
a.2. It does not require AR(MP(R)âMPT(R)) (in fact, I don’t use it at any point).
However, it does require AR(MPT(R)âMP(R)), in other words, it requires that For all propositions R, if R is metaphysically possible true, then R is metaphysically possible.
While that seems obvious to me, the other implication seems equally obvious to me, so if I’m going to assume something like A1 above, I would withdraw the proof, and assent to (X), as I mentioned (by the way, and out of curiosity, is AR(MPT(R)âMP(R)) controversial as well?)

Joshua,
I’ll give a proof of (X’) without Rule C (it wasn’t that long after all, since there was a faster way).
A few points, before I start (please let me know what you find controversial).
1. Some of the steps implicitly use first order theorems (i.e., formulas derivable from the axioms of a first order predicate calculus), so when I say ‘from premise H (for instance), I’m leaving implicit the use of those theorems. Proving all the theorems as well might make it way too long, and would take too long, so I’m hoping those aren’t controversial.
2. I’m assuming a classical first order predicate calculus. In particular, we have (Â¬Â¬PâP). I’m not saying that the proof works on non-classical logics (it would depend on the logic).
3. Notation:
a. An uppercase letter or an uppercase letter followed by a number represents a proposition.Â
b. MP(R): = R is metaphysically possible.Â
c. MPT(R): = R is metaphysically possibly true.Â
d. C(R): = R is contradictory.Â
e. E(R):H(R) := There exists at least one proposition R such that H(R) [for instance, E(R)/MP(R) means that there exists at least one proposition R such that R is metaphysically possible].Â
f: A(R):H(R) := For all propositions R, H(R).Â
4. I will accept the usual equivalences between connectives, and between quantifiers.
In particular, I’m using the equivalence between E(R):H(R) and Â¬(A(R):Â¬H(R)), and between (AâB) and Â¬(A&Â¬B).
Those equivalences are not theorems but just different ways of writing the same in mathematical logic, if one uses one primitive quantifier and two connectives, and defines the rest in terms of them.
I would say that the reason that we define them like is that we can tell that they’re equivalent by the meaning of the words and logic, and so we come up with formal systems that respect that, but I guess someone might find it controversial.
In any case, in a formal system, one may introduce all the connectives and quantifiers and then add more axioms to respect the equivalences, instead of defining some connectives and quantifiers in terms of the others, so I will accept them as theorems instead of different ways of saying the same (but it’s equivalent for the purpose of the proof).
5. (X’): It is metaphysically impossible that there is at least one proposition P, such that P is contradictory and P is metaphysically possibly true.
(X’) has the form “It is metaphysically impossible that Q”
Where Q is:
Q: There is at least one proposition P, such that P is contradictory and P is metaphysically possibly true.
So, formalizing it:
Q: E(R):(C(R)&MPT(R)).
6. So, in order to prove (X’), I would derive a contradiction from Q and premises that can be established (but I think you might disagree on them; at least, Rule C is not used) only by logic and using one’s intuitive grasp of the words:
P3: A(R):(MPT(R)âMP(R))Â
P4: A(R): (C(R)âÂ¬MP(R))
So, the proof:
Q: E(R):(C(R)&MPT(R))
P3: A(R):(MPT(R)âMP(R))Â
P4: A(R):(C(R)âÂ¬MP(R)).
1. A(R):(Â¬MP(R)âÂ¬MPT(R)) [from p3]
2. {(A(R):(C(R)âÂ¬MP(R)))&(A(R):(Â¬MP(R)âÂ¬MPT(R)))}â{(A(R):(C(R)âÂ¬MPT(R)))}} [first order theorem].
3. A(R):(C(R)âÂ¬MPT(R)) [from P4, 1. and 2.]
4. A(R):Â¬(C(R)&Â¬Â¬MPT(R)) [from 3.]
5. A(R):Â¬(C(R)&MPT(R)) [from 4]
6. Â¬(A(R):Â¬(C(R)&MPT(R)) [from Q].
7. (A(R):Â¬(C(R)&MPT(R))&Â¬(A(R):Â¬(C(R)&MPT(R)))
That’s a contradiction.

I am trying to construct a metaphysics which is consistent with QM (with no âcorrectionsâ to the theory) and which would satisfy me more than the other interpretations if I were a scientific realist. I try to assume as little as possible. As the only consciousness I know does change slowly I assume a long E since thatâs all I need. But nothing particularly important rides on the exact value of Eâs duration. Had I used one thousandth of a second instead of one tenth of second the argument would remain the same.

In other words, is it possible that the physical state of a brain changes while the conscious state remains the same?

Thatâs my assumption. Why do you think itâs problematic? Thatâs how things seem to stand from the subjective point of view (since conscious experience changes tenths of orders of magnitude slower than with Planck time), and to my knowledge there isnât any scientific evidence against it.
But I can see that some scientific realists may be committed to the identity theory of mind and dislike a large E. In the context of our discussion then we may lower E to the Planck time e, which is the lowest time span required for physical change, and assume that physical and conscious states change in step even if we are not aware of it (which is kind of a contradiction, isnât it?)

That seems to depend on the size of the universe.

It may be the case that B is not constant but grows with time. Still this does not affect my description of what happens at a particular point in time.

Are you ruling out an infinite universe?

I donât, for I donât see how it matters. But since thinking about infinities is a risky business, and since there isnât really any good evidence that the universe is infinite, for discussionâs sake I assume a finite one.

on this account, it seems the probability that there will be a Boltzmann brain at tb+E is, according to a probabilistic interpretation of QM, no more than 1/B, but on Volos, the probability that a Boltzmann brain will exist at tb+E is 1.

1/B of the successor states at tb+E will include at least one Boltzmann brain. On Volos, the state of the observable universe at tb+E will include conscious Boltzmann brains. And with probability very close to 1 that state will include just one very primitive conscious Boltzmann brain.

So, assuming Volos, we would need to separate two probabilities: the correct probability given by Volos, and the fake probability given by QM, which are vastly different.

I am not quite sure which two probabilities you refer to. QMâs wavefunction at tb+E determines which states of the universe include complex brains in them (whether Boltzmann or biological). We may call such states âcandidate statesâ, for on Volos one of these states will become the state of the observable universe at tb+E. The indeterministic mechanism by which one of the candidate states become observable depends of the weighting factor of the candidate states (the squared amplitude of the wavefunction, which on the epistemic interpretations of QM represents probabilities). Hereâs an example. Suppose at tb+E there are 4 physical states of the universe within the superposition, which I here represent by a letter and its associated weight.
a:0.1 â b:0.5 â C:0.3 â D:0.1
Now Volos identifies which states contain complex brains in them (here represented by upper case letters) and then uses their weights probabilistically to pick one of them. Thus at tb+E the state of the observable universe will be D with 0.75 probability, and E with 0.25 probability. States âaâ and âbâ are of universes where no complex brains exist (perhaps because all humans are destroyed by the accidental explosion of a doomsday machine). And among those states that according to QM may be observable, namely âCâ and âDâ, we shall observe âCâ thrice as probably than âBâ â exactly as QM predicts.

Volos introduces very significant changes to [QM]

Not at all. Volos (as any interpretation must) adds ontological stuff to QM but changes nothing in the mathematical theory itself. Nor does Volos entail phenomena that deviate from QMâs predictions (none of the interpretations of QM should). On Volos, QMâs wavefunction of the universe remains unmodified for all time, and is used at each point in time to specify both the physical states the universe is in and to specify the observable state among them.
I want to argue that compared to other interpretations the ontological stuff Volos adds is minimal. For example, Bohmâs interpretation adds an additional vastly complex as well as non-local guiding wave. MWI adds the claim that the observable universe around us is continuously splitting itself into a huge number of versions, versions we continue experiencing as versions of us within them. Ontological Copenhagen adds local collapses (i.e. removal from reality) of the wavefunction. GRW not only modifies QM (and thus shouldnât really be called an interpretation of QM) but does this by introducing new fundamental physical constants.
Which is not to say that Volos ontological additions arenât weird. What most bothers me in Volosâs mechanism is the identification of states of the universe with consciousness expressing properties (CEPs or âcomplex brainsâ) in them. The picture I visualize is that of states of the universe with CEPs being in some way âheavierâ and thus sinking into a plateau where one of them becomes âobservableâ. But we tend to think of CEPs as strictly local affairs within very small physical systems such as our brain â so itâs weird that their presence should have such a momentous ontological effect on the whole of the state of the universe.
Now I donât object to the claim that modifications to QM (such as GRW) produce a picture of reality which is more palatable to the scientific realist than Volos. But from the point of view of what I am trying to accomplish, these ontologies are not in the competition, since they donât interpret QM. In any case, one thing that modern physics has shown is that nature does not seem to care about our metaphysical assumptions, and thus the hypothesis that an alternative to QM designed solely to satisfy some peoplesâ metaphysical assumptions will prove to be right appears to have a low prior probability.
Finally, I wonder if you agree that the fact that our planet does not look like a Boltzmann planet is very strong evidence against MWI (or MMI). The idea is that at any point in time where conscious beings exist in the massive superposition virtually all of them observe a Boltzmann environment (i.e. one without any signs of geological or biological past) and not an environment like the one we do.

I am trying to construct a metaphysics which is consistent with QM (with no âcorrectionsâ to the theory) and which would satisfy me more than the other interpretations if I were a scientific realist. I try to assume as little as possible. As the only consciousness I know does change slowly I assume a long E since thatâs all I need. But nothing particularly important rides on the exact value of Eâs duration. Had I used one thousandth of a second instead of one tenth of second the argument would remain the same.

Okay, so what if a conscious Boltzmann brain is destroyed in less than that time?
In other words, let’s say at some time t, there is a Boltzmann brain BB(t), which is conscious at that time and for the first time. The state of consciousness does not change up till t+E. Let’s say it’s conscious at t+E as well. What happens if BB(t) no longer exists at t+E+E/2?

Thatâs my assumption. Why do you think itâs problematic? Thatâs how things seem to stand from the subjective point of view (since conscious experience changes tenths of orders of magnitude slower than with Planck time), and to my knowledge there isnât any scientific evidence against it.

Consider the case above. At t+E+E/2 there are no conscious brains in the universe, but there is still consciousness, and there is collapse of the wave function at every time.
Would unembodied consciousness cause collapse as embodied consciousness, or would the specific Volos function take over?
For instance, if there are Boltzmann brain with the capability for consciousness in the superposition at t+E+E/2+e, will one of those get selected? (and now I’m using ‘e’ to denote a Planck Time).

But I can see that some scientific realists may be committed to the identity theory of mind and dislike a large E. In the context of our discussion then we may lower E to the Planck time e, which is the lowest time span required for physical change, and assume that physical and conscious states change in step even if we are not aware of it (which is kind of a contradiction, isnât it?)

I don’t see how. The changes in consciousness need not amount to an apprehension that a change in consciousness has occurred.
In any case, there might be changes in some other brain’s consciousness. In other words, even if the physical states changed with e and the mental states of every conscious organism change with E, it may well be that the sum (or set, or whatever one calls it) of consciousness of the whole universe change with e. Even if Brain1 is stuck from t1 to t1+E in the same state, it might be (at least, your exposition of Volos doesn’t seem to rule it out) that Brain 2 becomes conscious at t1+e, etc.

I donât, for I donât see how it matters. But since thinking about infinities is a risky business, and since there isnât really any good evidence that the universe is infinite, for discussionâs sake I assume a finite one.

As I understood it, you seemed to be making an argument based on the number of states containing simple Boltzmann brains vs. the number containing Boltzmann planets, etc., apparently assuming equal probability for each state. But the assumption of equal probability does not work if the universe is infinite.
Anyway, the probability function would be a problem anyway.

On Volos, the state of the observable universe at tb+E will include conscious Boltzmann brains. And with probability very close to 1 that state will include just one very primitive conscious Boltzmann brain.

Yes, but on QM, that is not the probability.
On Volos, the probability of at least one Boltzmann brain at tb+E is 1, and the probability of exactly 1 Boltzmann brain is almost 1.
On QM, the probability of at least Boltzmann brain at tb+E is less than 1, and in fact, at some times the difference will be huge.
For instance, and when talking about a single brain, you mentioned before:

Â Since on Copenhagen metaphysics consciousness cannot exist in a superposed state, C(s2111) and C(s2112) cannot coexist. So nature is forced to choose one physical state. On the naturalistic view nature does this blindly by throwing dice and picking one of the three states (while respecting the respective amplitude probabilities of the three physical states). Suppose these probabilities are 0.6 for s2111, 0.2 for s2112, and 0.2 for s2113. As luck would have it the consciousness expressing state s2112 is indeterministically chosen. (Had s2113 been chosen then the brain would transit back to a non-conscious state.)Â

Now, let’s say that we’re kind of in the middle of the Boltzmann brains era, and at some t1, there is exactly one Boltzmann brain BB1, and it is conscious.
Let’s say that the probability that that brain will continue in a state capable of consciousness at, say, t1+E, is 0.5, according to QM probabilities (i.e., respecting probabilities based on the amplitude)
Then, the probability that there will be a brain capable of consciousness at t1+E may well be under 0.6, according to QM probabilities (it’s the probability that either BB1 continues to be capable of consciousness, or yet another Boltzmann brain emerges, but the latter is very improbable in a finite universe unless it’s really gigantic).
So, the Volos-probability that there will be at least one brain capable of consciousness at t1+E is 1, and the Volos-probability that there will be exactly one brain capable of consciousness at t1+E is almost 1.
On the other hand, the QM-probability that there will be at least one brain capable of consciousness at t1+E is under 0.6, and the QM-probability that there will be exactly one such brain is slightly less than the previous one.
Also, unless the universe is really big, the difference is in some cases much bigger than that.
You might be able to reduce the difference by including increasingly large universes, but you won’t get a QM-probability=1 (of at least one brain capable of consciousness at t1+E) unless the universe is infinite.
So, in a finite universe, QM-probability and Volos-probability are different. So, it seems that Volos is a modification to QM, rather than an interpretation.
However, unlike other modifications, it’s not entirely clear what function Volos is using to compute probability (though it seems to be based on number of occurrences in the superposition, or something like that), and has a number of other disadvantages in my assessment, some of which I mentioned before.
On the other hand, in an infinite universe, I don’t know how you would construe Volos, and you’re assuming a finite universe in the first place. So, I will wait for your reply before I analyze the infinite case.

I am not quite sure which two probabilities you refer to. QMâs wavefunction at tb+E determines which states of the universe include complex brains in them (whether Boltzmann or biological). We may call such states âcandidate statesâ, for on Volos one of these states will become the state of the observable universe at tb+E. The indeterministic mechanism by which one of the candidate states become observable depends of the weighting factor of the candidate states (the squared amplitude of the wavefunction, which on the epistemic interpretations of QM represents probabilities).

I’m not sure I’m making my point clearly enough, then.
Let me try another example:
Let’s say that the Boltzmann brain that is conscious at tb is very unstable (which is very plausible), and the probabilities (using a probabilistic interpretation of QM) that it will remain capable of consciousness at, say, tb+100E is less that 1/1000000.
(Here, I’m using probability as you did before in an earlier posts, when you mentioned the probability that a brain would go back to unconsciousness, though I’m counting only multiples of E in order to keep the objections separated for the sake of clarity; in other words, the QM-probability is the one that uses the squared amplitude of the wavefunction).
Now, let’s say that the QM-probability that there will be at least one conscious brain other than that one at tb+100E is less than 1/1000000. Then, the QM-probability (i.e., the probability under a probabilistic interpretation of QM, which respects the amplitude) at there will be at least one conscious brain at tb+100E is less than 1/500000, but the Volos-probability that there will be at least one brain capable of consciousness at tb+100E is 1, and the Volos-probability that there will be exactly one such brain at tb+100E is almost 1.
Then, QM-probability that there will at least one brain capable of consciousness at tb+100E is far less than the Volos-probability that there will be one such brain. As I mentioned above, you can reduce the difference by increasing the size of the universe, but on a finite universe, the probability will not become 1.

Hereâs an example. Suppose at tb+E there are 4 physical states of the universe within the superposition, which I here represent by a letter and its associated weight.
a:0.1 â b:0.5 â C:0.3 â D:0.1
Now Volos identifies which states contain complex brains in them (here represented by upper case letters) and then uses their weights probabilistically to pick one of them. Thus at tb+E the state of the observable universe will be D with 0.75 probability, and E with 0.25 probability. States âaâ and âbâ are of universes where no complex brains exist (perhaps because all humans are destroyed by the accidental explosion of a doomsday machine). And among those states that according to QM may be observable, namely âCâ and âDâ, we shall observe âCâ thrice as probably than âBâ â exactly as QM predicts.

But QM does not rule out states in which no complex brain remains.
If we go with a probabilistic interpretation of QM, and if also the universe is finite, there is a non-zero chance that in the future there will be no complex brains (why not?).
In other words, even though the ‘tagging’ is the Volos account of the collapse of the wavefunction, Volos is tagging states with probabilistic assignments that are different from the probabilistic assignments on a probabilistic interpretation of QM that uses the squared amplitude of the wavefunction.

Now I donât object to the claim that modifications to QM (such as GRW) produce a picture of reality which is more palatable to the scientific realist than Volos. But from the point of view of what I am trying to accomplish, these ontologies are not in the competition, since they donât interpret QM. In any case, one thing that modern physics has shown is that nature does not seem to care about our metaphysical assumptions, and thus the hypothesis that an alternative to QM designed solely to satisfy some peoplesâ metaphysical assumptions will prove to be right appears to have a low prior probability.

But what you call ‘metaphysical assumptions’, may well be probabilistic assessments of the evidence (of course, I’m talking about epistemic probability here, which is intuitively assessed).
In any case, if an alternative to QM is not at this point distinguishable from it, I would say that the matter of the intention of those proposing it is not particularly important in order to assign it a (epistemic, of course) probability.
Also, in order to assess the probability of a certain hypothesis, the mathematical model is not the only thing to assess, but the ontological consequences as well (if not predominantly).
If (QM including its most probable ontology) is less probable than (GRW including its most probable ontology), then so be it. And if QM+(At least one of its ontologies) is less probable than the same for GRW, then also so be it.
Those probabilistic assessments are based on a number of factors, considering the evidence available to each person. I don’t take a stance in favor of GRW or Weinberg’s proposal at this time; I just do not know. But I don’t see any persuasive reason to give them less probability at the moment, either.

Finally, I wonder if you agree that the fact that our planet does not look like a Boltzmann planet is very strong evidence against MWI (or MMI). The idea is that at any point in time where conscious beings exist in the massive superposition virtually all of them observe a Boltzmann environment (i.e. one without any signs of geological or biological past) and not an environment like the one we do.Â

It would depend on how one assigns probability in that massive superposition/multiverse; it gets even more complicated if the universe is infinite.
I’m not an expert, and I don’t know enough about a number of issues to take a stance at the moment â though I do find MWI implausible, and MMI even more so -, but I will continue considering the matter.
Incidentally, a similar issue (not the same, but similar) appears to be under discussion in an eternally inflating universe (e.g., http://arxiv.org/abs/0808.3778 ).

Dianelos,
I think I get what’s going on:
After the collapse, you’re restricting the probabilities to states that contain complex brains in them, instead of computing probabilities over all of the physical states that the original collapsed state branches into, so states in which the first brain goes back to being unconscious are ruled out unless there is another Boltzmann brain that becomes conscious, and so on.
I don’t see how that would be an interpretation that uses the probabilities assigned by QM, since you’re eliminating a lot of physical states that would otherwise be among the open possibilities. Moreover, the choice of those states is based on whether there is something called ‘complex brain’, and that is not even defined in the theory, so I’m not sure how one would go about computing Volos probability.

Thanks Angra,
I agree that a proof is possible *using* other axioms, such as P4. You may reply that P4 is true by definition. But if we *define* impossibility so that P4 is true by definition, then I am back to wondering how we could, for instance, show the basic inference rules (such as double negation) are necessary, unless they, too, are packed into the definition of ‘metaphysically necessary’. In the end, I don’t see how *any* definition of ‘is metaphysically impossible’ or ‘is metaphysically necessary’ will be able to account for all the apparent cases. A while back, I asked Swinburne how to account for the necessity of ‘It is logically possible that donkeys exist’, and he ended up appealing to S5. But how do you account for the necessity of S5? I suppose you could build S5 (and other modal axioms) into an increasingly complex definition of ‘necessity’… but I have yet to see any such worked out definition (I suspect it would be infinitely long or merely schematic). And at any rate, it seems my grasp of necessity is prior to any grasp of any such definition.
(Sorry I didn’t reply sooner; I can only spare a few minutes every few days; but I appreciate your notes!)

But if we *define* impossibility so that P4 is true by definition, then I am back to wondering how we could, for instance, show the basic inference rules (such as double negation) are necessary, unless they, too, are packed into the definition of ‘metaphysically necessary’.

You mean, how you show that for any proposition P, the proposition DN(P) := (Â¬Â¬PâP) is metaphysically necessary?
We could say that that is strictly logically necessary, and that strict logical necessity entails metaphysical necessity, and that would be packed into the definition of’ ‘metaphysical necessity’.
By the way, do you hold that there are propositions such that it makes no sense to speak of terms, meaning, etc.?
Even without a specific definition of metaphysical possibility, I would say that the way I intuitively go about assessing metaphysical possibility (necessity, impossibility) seems to be based on strict logical possibility (necessity, impossibility) augmented with the meaning of the words (grasped intuitively), including the referents of rigid designators (except indirectly based on those, and which I already know, such as the fact that a negation of a necessary proposition is impossible), and that seems to be what I mean by metaphysical modality claims (the definition of metaphysical impossibility I proposed is an example of that).

In the end, I don’t see how *any* definition of ‘is metaphysically impossible’ or ‘is metaphysically necessary’ will be able to account for all the apparent cases.Â

As far as I can tell, the one I proposed deals with the cases presented so far, in the case of metaphysical impossibility.Maybe one could propose definitions of metaphysical possibility and necessity as well (which are equivalent to definitions based on impossibility (e.g., Q is necessary: = Â¬Q is metaphysically impossible), but are not the same), based on strict logical possibility, etc., augmented as suggested above.
Alternative, if we also define metaphysical necessity in terms of impossibilities (which may not be the most basic definition, but respects all cases), then my definition handles those cases as well.
For instance, in the case of NP(P), in order to see whether it’s metaphysically necessary, under a definition Q is necessary: = Â¬Q is metaphysically impossible, one would have to check whether Â¬(Â¬Â¬PâP) meets criteria C1 for metaphysical impossibility (i.e., the criteria I proposed).
That works, since Â¬(Â¬Â¬PâP) is strictly contradictory.
So, as far as I can tell, the definition I proposed plus a definition of metaphysical necessity based on that one does handle all the apparent cases we’ve tested so far. I’m not saying that that’s the most basic definition of metaphysical necessity, though I think that the definition of metaphysical impossibility I gave is the most basic definition, at least as I seem to grasp the term.

And at any rate, it seems my grasp of necessity is prior to any grasp of any such definition.

It might be prior to a conscious grasp of them, but still your concept depends on a more primitive concept of (perhaps) strict logical necessity.
Else, I do not know of any other means of assessing metaphysical possibility If you have any other means of looking for impossibilities, please let me know (since that might suggest a difference in our grasp of the terms).
Still, let’s say that you don’t have that concept of metaphysical necessity (possibility, impossibility), then I would say that there is a problem with the common language assumption, and I would ask how to go about trying to grasp the concept of metaphysical impossibility that you use.
In other words, if we actually tackle the matter differently when it comes to assessing metaphysical modality, that seems to provide evidence against the common language assumption as far as I can tell.

Volos doesnât say. While interpreting the world realistically I tend to think that actual conscious experience (or quales) are expressed by a complex brain, like drops of water falling of a drippy faucet. But Volos only says that at multiples of E one state with complex brains in it will become observable. Thus there is space of the details of the solution of the mind-body problem to fit in. To avoid this issue we may for discussionâs sake assume that E=e, the Planck constant.
Incidentally, BBs are highly unstable only within some state history. Within the massive superposition any BB remains for ever. There will even be a state history branching out of a state with a BB where this BB will experience Mozartâs live over and over again.

For instance, if there are Boltzmann brain with the capability for consciousness in the superposition at t+E+E/2+e, will one of those get selected?

No. The Volos algorithm only applies to the state of reality (the set of states of the universe within the superposition) at multiples of E.

The changes in consciousness need not amount to an apprehension that a change in consciousness has occurred.

But if a change in consciousness is not apprehended then in what sense is that a âchange in consciousnessâ?
It seems to me that when we speak of consciousness we speak of the deliverances of our conscious experience of life. By definition if something is not experienced by me it does not belong to my consciousness. I donât experience the state of each electron in my brain, so they do not form part of my consciousness. The CEP must be some complicated function over the states of the particles in my brain. But since in fact my consciousness does not change as fast as CEP (since physical states change with the Planck time) it seems to me that any identity theory of mind is false on its face.

you seemed to be making an argument based on the number of states containing simple Boltzmann brains vs. the number containing Boltzmann planets, etc., apparently assuming equal probability for each state.

Each state within the massive wavefunction comes with a weighting factor, which is interpreted probabilistically when using QM in real life (i.e. when interpreting it epistemically). Thus the weighting factor of a Boltzmann brain materializing nearby is much smaller that of a Boltzmann planet materializing nearby, reflecting the fact that it is much more probable to observe the former than the latter. That weighting factor though is very much taken into account by Volos. Thatâs how Volos guarantees that the state of the observable universe will be such that the phenomena we observe fit with QMâs predictions (as long as most states branching out of a particular observable state contain complex brains in them â see bellow).

On QM, the probability of at least Boltzmann brain at tb+E is less than 1, and in fact, at some times the difference will be huge.

Now I see your point. Youâre right. If we were there searching through the observable universe in its âBoltzmann epochâ (i.e. between tb and t0) then we would always find a primitive BB somewhere, which on QM would be highly unlikely. But, on Volos, if we were there then the BBs would disappear (as they did disappear from the observable universe once the first biological brain became conscious at t0). So itâs not in fact true that we would observe something that contradicts QM.
The claim that Volos makes is that no *actual observation* by us will contradict QMâs predictions. (A claim, incidentally, that MWI and MMI cannot make since on them there are actual observations of the Statue of Liberty swimming around Manhattan.) A state of the universe without complex brains in it will not be made the one observable, but then itâs not observable any way.
Actually, if one wants to push the issue, there is on Volos at least the possibility that QM predictions are contradicted on observation: Assume only a single conscious brain survives, that of a scientist studying her own brain. Further assume that CEP is a very unstable property, so that if CEP exists at time t the probability that it will continue to exist at t+E is only 1%. Now on Volos the scientist would not subjectively find anything amiss. Even though 99% of the states of the universe at any t+E include her brain in a zombie state, Volos will pick as the next state of the observable universe one where her brain still has CEP. But suppose now our scientist studies the CEP property in her brain. She will find that it is always there, whereas QM predicts it should quickly decay. Thus she will have observed an actual contradiction with QM.
The interesting implication for philosophy of science is that it may be the case that a true scientific theory is definitely contradicted by actual observation. Incidentally the same holds for MWI and MMI were right now people are lined up on the shore of Hudson river watching the Statue of liberty swimming in it, in clear violation of about every law written in physics books.

Then, the probability that there will be a brain capable of consciousness at t1+E may well be under 0.6,

If, starting at the state you described for t1 with a BB in it, one were to probabilistically (i.e. randomly but taking into account the weighting factors) choose a state history that branches out of it, then, yes, the probability of finding a BB brain at t1+E will be 0.6. And Volos will pick one of these states, ignoring the states in the 0.4 rest of the distribution function. Thatâs why at t1+E the state of the observable universe will again include a BB brain.

If we go with a probabilistic interpretation of QM, and if also the universe is finite, there is a non-zero chance that in the future there will be no complex brains

Right. Whereas on Volos there will always be conscious beings in the observable universe. Or, to put it differently, on Volos there will always be an observable universe. But that also holds on MWI, the difference being that on Volos there is only one never ending observable universe (with conscious beings in them), whereas on MWI there are many such universes. Indeed so many that each one of us (in the sense of continuous and self-aware experience) will live for ever. Volos at least avoids that last piece of absurdity, never mind gross violation of QMâs probabilistic predictions in such universes.
Letâs see if on Volos we can find within the deep future some actual observational contradiction with QM. From what we today think we know it seems that after many billions of years no biological brains, indeed no stable brains of any kind, will be physically possible. As far as I can see Boltzmann brains will still be possible though, so we would enter a second Boltzmann epoch of just one primitive conscious experience obtaining. Is there a period between now and the start of the second Boltzmann epoch, in which period intelligent beings still exist and find that this contradicts the probabilistic predictions of QM? I am not sure about this, but it seems not improbable. The Volos metaphysics is favoring states that include consciousness, and this might someday become noticeable. QM on the other hand doesnât. So suppose this state of affairs does obtain. Suppose in the deep future some intelligent beings wonder about their own âmagical-likeâ persistence, against QMâs predictions. Would this state of affairs falsify or rather confirm Volos? It seems to me clear that it would confirm it. Indeed it would confirm both Volos and QM, since Volos uses QMâs wavefunction for the universe without modifications, and just tags observational status on one state history in it.
Stepping back from Volos, what I think the above analysis shows is this: Even if one understands the physical sciences strictly as being about discovering mathematical order within physical phenomena, one cannot confirm or disconfirm a physical theory independently from metaphysics. Ultimately, only the conjunction of scientific theory and its ontological interpretation can be confirmed or disconfirmed by observational evidence.
More specifically, in the context of the debate about whether theism or naturalism is more probably true, given the body of scientific knowledge âSâ the question that should be investigated is not: p(T | S) versus p(N | S), but rather p( T | S and O(S) ) versus p( N | S and O(S) ) where âOâ stands for âontological interpretationâ, or rather the ontological interpretation that maximizes the respective probabilities. Thus scientific evidence by itself cannot be evidence *for* naturalism or for theism.

If (QM including its most probable ontology) is less probable than (GRW including its most probable ontology), then so be it.

Right, I agree. My point still stands though. First, historically speaking, metaphysical assumptions or intuitions have proved to be mostly bad guides for physicists. Secondly, as a matter of scientific tradition if you will, physicists are not supposed to add complexity to a theory, let alone new fundamental constants, just in order to make it fit with some ontology they happen feel comfortable with. Thirdly, QMâs most natural and conceptually unproblematic ontologies are arguably those in which reality âcomputesâ quantum phenomena, a view which is consistent with idealism and with some forms of naturalism also â but not with scientific realism. According to some critics Bohmâs interpretation is really the idea that physical reality consists of just such a computer which produces the observations QM predicts.
Anyway, fair enough, GRW is on the table â so letâs hope that it will be put the test. And hope that if it is falsified by experiment nobody will use the new data to modify the theory or its respective ontology in order to make the new evidence fit. At some point I think philosophers should put down ground rules about what should be considered reasonable and what shouldnât.

Incidentally, BBs are highly unstable only within some state history. Within the massive superposition any BB remains for ever. There will even be a state history branching out of a state with a BB where this BB will experience Mozartâs live over and over again.

Yes, but those are much less common, and while Volos does not say exactly how it chooses, it seems that we know enough to tell that (just as there will probably be one at a time, unless the universe is really big), the vast majority of them will be unstable.

But if a change in consciousness is not apprehended then in what sense is that a âchange in consciousnessâ?

I suppose at this point it’s a matter of what one means by ‘being aware of it’ and ‘consciousness’.
I got the impression that you required a particular kind of conscious process, like being aware that something changes, at a conscious level. It may well be that as particles change, so do forms of basic consciousness in our brains that ‘we’ are not aware of (e.g., consider split brains; I would not rule out that the part of the brain that is ‘rebellious’ also has some level of consciousness, even if other parts of the mind are not aware of).

It seems to me that when we speak of consciousness we speak of the deliverances of our conscious experience of life. By definition if something is not experienced by me it does not belong to my consciousness. I donât experience the state of each electron in my brain, so they do not form part of my consciousness. The CEP must be some complicated function over the states of the particles in my brain. But since in fact my consciousness does not change as fast as CEP (since physical states change with the Planck time) it seems to me that any identity theory of mind is false on its face.

It depends on what you mean by ‘identity’; I usually find them false because the meaning of the words is not what they propose, but on the other hand, I see no good reason to think that there is some soul or something. Different states of particles can change at different speeds, in any event.

Now I see your point. Youâre right. If we were there searching through the observable universe in its âBoltzmann epochâ (i.e. between tb and t0) then we would always find a primitive BB somewhere, which on QM would be highly unlikely. But, on Volos, if we were there then the BBs would disappear (as they did disappear from the observable universe once the first biological brain became conscious at t0). So itâs not in fact true that we would observe something that contradicts QM.

Right, though the Boltzmann brains did not strictly disappear on Volos, it seems to me. It’s just that we don’t have the means of finding any remains.

The claim that Volos makes is that no *actual observation* by us will contradict QMâs predictions. (A claim, incidentally, that MWI and MMI cannot make since on them there are actual observations of the Statue of Liberty swimming around Manhattan.) A state of the universe without complex brains in it will not be made the one observable, but then itâs not observable any way.

Volos says that very probably, we will see no such observations, though it does not tell us exactly how much (since it does not give a definition of ‘brain’ to be applied; that’s a difficulty).
Whether MWI can properly make that claim depends on factors such as whether the Born rule can be derived on MWI. The matter is debated, it seems to me, but for now they don’t have it (I don’t defend MWI, btw).

Actually, if one wants to push the issue, there is on Volos at least the possibility that QM predictions are contradicted on observation: Assume only a single conscious brain survives, that of a scientist studying her own brain. Further assume that CEP is a very unstable property, so that if CEP exists at time t the probability that it will continue to exist at t+E is only 1%. Now on Volos the scientist would not subjectively find anything amiss. Even though 99% of the states of the universe at any t+E include her brain in a zombie state, Volos will pick as the next state of the observable universe one where her brain still has CEP. But suppose now our scientist studies the CEP property in her brain. She will find that it is always there, whereas QM predicts it should quickly decay. Thus she will have observed an actual contradiction with QM.

Pretty neat. It would be pretty difficult to test, of course.

Right. Whereas on Volos there will always be conscious beings in the observable universe. Or, to put it differently, on Volos there will always be an observable universe. But that also holds on MWI, the difference being that on Volos there is only one never ending observable universe (with conscious beings in them), whereas on MWI there are many such universes. Indeed so many that each one of us (in the sense of continuous and self-aware experience) will live for ever. Volos at least avoids that last piece of absurdity, never mind gross violation of QMâs probabilistic predictions in such universes.

The issue of the probabilist predictions depends on whether the Born Rule can be derived on MWI, or somehow the problem can be corrected, but otherwise, you’re right.
On the other hand, I would say that Volos results in other absurdities, like the zombie world, etc.; but we’ve discuss that before, and it seems our intuitive probabilistic assessment of those particular cases (i.e., how absurd it is) is different. I’ll leave it at that.

Stepping back from Volos, what I think the above analysis shows is this: Even if one understands the physical sciences strictly as being about discovering mathematical order within physical phenomena, one cannot confirm or disconfirm a physical theory independently from metaphysics. Ultimately, only the conjunction of scientific theory and its ontological interpretation can be confirmed or disconfirmed by observational evidence.

Right; it’s just that I would be more inclined to include the ontological interpretation as part of science, or rather, the task of coming up with a correct interpretation, or also more precisely, as close to correct as we can.
Still, this is to some extent a matter of terminology, since the issue is that people will have to use different means (reasoning, experiments, etc.) and then make (epistemic) probabilistic assessments based on them.

Right, I agree. My point still stands though. First, historically speaking, metaphysical assumptions or intuitions have proved to be mostly bad guides for physicists. Secondly, as a matter of scientific tradition if you will, physicists are not supposed to add complexity to a theory, let alone new fundamental constants, just in order to make it fit with some ontology they happen feel comfortable with. Thirdly, QMâs most natural and conceptually unproblematic ontologies are arguably those in which reality âcomputesâ quantum phenomena, a view which is consistent with idealism and with some forms of naturalism also â but not with scientific realism. According to some critics Bohmâs interpretation is really the idea that physical reality consists of just such a computer which produces the observations QM predicts.

1. I don’t know which assumptions you call ‘metaphysical’, but I would say that philosophers don’t have a better track record on interpreting the mathematical models, as well as making ontological claims.
Still, I would tend to include that as science regardless of the issue of what people should study in order to be good at it.
2. As I mentioned before, what you call ‘being comfortable with’ I would call an intuitive probabilistic assessment, etc.
In any case, it seems to me that scientists often propose that, but regardless of who does it, my point stands that they should take the points I mentioned under consideration.
3. Personally, I would have to disagree with that, but it would take too long to debate, and soon I will probably have to step out of the thread, due to RL commitments (my vacation is almost over).
So, I’ll leave it at that.

Angra,As far as I can tell, the one I proposed deals with the cases presented so far, in the case of metaphysical impossibility.
It’s tempting to revisit cases. Here’s one that seems clear to me: “someone becomes the empty set”. Nothing in logic allows us to deduce that no one takes on the properties of an empty set. You may say that we can tell a priori that this is impossible once we understand the meaning of the terms. Well, sure: it’s a clear case, after all. A less clear case would be “there can’t be extended simples”. Either it or its denial is impossible (by s5), but neither it nor its denial can be determined to be impossible by your criteria (as far as I understand your criteria). Also, many, many metaphysical disputes are over alleged necessary truths that cannot be discerned just by examining definitions of terms (such as, objects persist by perduring, presentism is false, composites are identical to their parts, mental properties supervene upon physical properties, and so on).
As I suggested before, I no more have a general criteria by which to deduce possibility and necessity in every case than I have a criteria to deduce truth and falsity in every case. Life is more complex. 🙂

Joshua,
I dealt with a similar case in an earlier reply to Dianelos, in which the way ‘transforms’ is used, but ‘becomes’ is similar, since it indicates (again, meaning of the words) a process of transformation, at least in this case (e.g., ‘She becomes the President’ does not indicate that, but context indicates the meaning of ‘becomes’ one is to consider, which is the sense of ‘transforms’).
I want to show it’s impossible for a person to become the empty set.
Let’s say that there is a person who becomes the empty set.
So, I would imagine a scenario as follows: at some time t0 there is a person (say, Alice, to give her a name), who then undergoes a certain process of change (it can be very fast), such that there is kind of causal or ontological continuity at any point in the process (i.e.,Â at least, some of the things Alice or the following things in the process are made of continue to exist from one stage in the process to the next, if there is no temporal density, and for a small interval if there is, or at least there is some causal continuity).
The specific kind of causal or ontological continuity that is required is very difficult to characterize, as is a conceptual analysis of the term ‘transforms’ (in the relevant sense, which is not the sense of mathematical transformation I think); maybe ontological continuity is required always, but in in any case, the issue is that at the end of the process, instead of Alice, what we have some other entity, not an abstraction.
So, if we assume that what we have at the end of it is the empty set, that’s a contradiction.

Â A less clear case would be “there can’t be extended simples”.

Sure, but that’s because I’m not sure what you mean by ‘extended’ and ‘simples’. The point is that there is vagueness in the words in question (or at least, I’m not familiar enough with them to tell).

Either it or its denial is impossible (by s5), but neither it nor its denial can be determined to be impossible by your criteria (as far as I understand your criteria).

I don’t see why not. That I can’t determine it now because I don’t know the meaning of the terms enough (or just because it’s difficult) does not mean it’s an exception.
I’m probably not tracking you here, but for instance, there are plenty of cases in which we don’t know whether a formula follows from some axioms in a first order theory and/or its negation follows, or neither does, and it’s difficult to figure it out, applying the rules of derivation of formulas, but that does not mean that the criteria that a formula follows from some axioms iff there is a certain sequence of formulas, etc., is not correct.

Also, many, many metaphysical disputes are over alleged necessary truths that cannot be discerned just by examining definitions of terms (such as, objects persist by perduring, presentism is false, composites are identical to their parts, mental properties supervene upon physical properties, and so on).

In some of those cases (actually, in most of those cases), I think imprecision is a problem (e,g, what’s a physical property? What’s a composite?), and in others, there may also be a rigid designator (involving time, for instance; otherwise), but in any case, I would ask for any other means of discerning them.
For instance, let’s consider the case of composites. If someone intends to deny that composites are identical to their parts, she’ll probably try to come up with counterexamples; but in those counterexamples, the person assessing them is only using logic and her intuitive grasp of the terms (including rigid designators) as far as I can tell. If you know of any other means often used and accepted, I’d be interested to know examples.

As I suggested before, I no more have a general criteria by which to deduce possibility and necessity in every case than I have a criteria to deduce truth and falsity in every case. Life is more complex. 🙂

Do you have any specific examples (rather than a general criteria) of procedures that are accepted as usable and that are not limited to logic, meaning of the terms, and rigid designators?
That might provide evidence against the concept I suggested.

it’s just that I would be more inclined to include the ontological interpretation as part of science, or rather, the task of coming up with a correct interpretation, or also more precisely, as close to correct as we can.

Itâs a matter of definition. But since the philosophical discourse is already confusing enough, Iâd rather keep âphysical sciencesâ to refer exclusively to âthe discovery of patterns within the set of physical phenomenaâ â and leave metaphysics to deal with how reality is given in part the deliverances of the physical sciences. Metaphysics is very difficult and I think itâs clear that the deliverances of the physical sciences (in my sense) are not adequate for justifying belief.
Of course scientists are free to also work in metaphysics if they like (a few of them do and call it the âfoundationsâ of physics). Sticking to the hunting of patters is interesting enough and practically exhausts the usefulness of scientific work. It would serve us all better if scientists would not dedicate too much of their time to trying to understand what it all means. But they donât anyway, so I am worried about a non-problem.

The thought behind it is this:
1. All understanding is ultimately grounded in personal experience.
2. Understanding a meaning is a kind of understanding.
3. Therefore all meaning is ultimately grounded in personal experience.
I justify premise 1 by examples, and by pointing out the absence of counterexamples. Indeed what is there to ultimately ground understanding but experience? (By âultimately grounding inâ I mean the last and conclusive answer to a series of searching questions when one is asked about why one holds a particular belief. I am not here referring to justification; the reason one has for holding a belief may be all wrong, but it must ultimately be grounded in something.)
There is also a pragmatic argument to be made:
Take Joshuaâs first example âThere are no people who transform into a prime numberâ and consider the simpler case âJohn transformed into a prime numberâ. What does it mean? How would the fact that John transformed into a prime number possibly affect anything in my experience of life? Now or in the future? At least in principle? If no answers are forthcoming then what profit is there in even considering that issue? Why are we even discussing it?

The thought behind it is this:
1. All understanding is ultimately grounded in personal experience.Â
2. Understanding a meaning is a kind of understanding.Â
3. Therefore all meaning is ultimately grounded in personal experience.
I justify premise 1 by examples, and by pointing out the absence of counterexamples. Indeed what is there to ultimately ground understanding but experience? (By âultimately grounding inâ I mean the last and conclusive answer to a series of searching questions when one is asked about why one holds a particular belief. I am not here referring to justification; the reason one has for holding a belief may be all wrong, but it must ultimately be grounded in something.)

You mean what caused one to have a particular belief?
If so (if not, please clarify), it’s an interesting question. Newborn babies learn and gain beliefs (or fetuses, or whatever starts having beliefs). Did experience come first, or did belief come first? Is there a fact of the matter?
At any rate, there is no need to settle that, since (in the sense of causation), since all you need is for that to be true of the understanding of a meaning of a term, and that seems to be very plausible.

Take Joshuaâs first example âThere are no people who transform into a prime numberâ and consider the simpler case âJohn transformed into a prime numberâ. What does it mean? How would the fact that John transformed into a prime number possibly affect anything in my experience of life? Now or in the future? At least in principle? If no answers are forthcoming then what profit is there in even considering that issue? Why are we even discussing it?Â

I’m rather sympathetic to the idea of not discussing some things that are less than clear, at least until one can make them clear enough to reduce the risk of significant miscommunication, etc., and also not (usually) not discussing cases like that.
That said, the reason I’m discussing the matter now (more precisely, now we’re discussing the case in which someone becomes the empty set) is that I was actually trying to understand the meaning of some of the terms used by Joshua (specifically, ‘metaphysically impossible’), and proposed a definition that as far as I can tell matches my intuitive grasp of the term.
Joshua offered the case of a person becoming the empty set as a potential counterexample to my account; since in my assessment the account still works in that case, I’m explaining why I think so.
What are the practical consequences of John’s transforming into the empty set? (or a prime number).
I don’t think that that’s possible, so none.
But on the other hand, there are practical consequences of an assessment of what ‘metaphysically impossible’ means, or at least whether a certain criteria works always, etc. (e.g., regarding how to approach arguments from contingency).

Angra,the issue is that at the end of the process, instead of Alice, what we have some other entity, not an abstraction.
I just can’t see how this part falls out of the definition of terms. Of course, I can “see” how the proposition expressed by the words you’ve used is true. But that’s just to say that I can tell that the modal claim in question is true, just when I think of it.Sure, but that’s because I’m not sure what you mean by ‘extended’ and ‘simples’.
For my part, the term ‘extended’ is primitive, and I take myself to know its meaning as a result of acquaintance with extended things. ‘Simple’ gets defined in terms of ‘part’, where ‘part’ is primitive. I confess I would be very surprised if all the debates in contemporary metaphysics over alleged necessary truths merely turned on a confusion of terms. But of course, I am an “insider” (metaphysics is my area of specialization); so I am certainly biased. 🙂For instance, let’s consider the case of composites. If someone intends to deny that composites are identical to their parts, she’ll probably try to come up with counterexamples; but in those counterexamples, the person assessing them is only using logic and her intuitive grasp of the terms (including rigid designators) as far as I can tell. If you know of any other means often used and accepted, I’d be interested to know examples.
To avoid (solve?) sorites puzzles, perhaps.Do you have any specific examples (rather than a general criteria) of procedures that are accepted as usable and that are not limited to logic, meaning of the terms, and rigid designators?
Hmmm, you mean like inference to the best explanation, a priori intuition, theoretical cost counting, etc.?
(I edited this comment.)

I just can’t see how this part falls out of the definition of terms. Of course, I can “see” how the proposition expressed by the words you’ve used is true. But that’s just to say that I can tell that the modal claim in question is true, just when I think of it.

I don’t have a precise definition of ‘transforms’ or ‘becomes’ (in this context) (e.g., I didn’t explain the continuity in detail), I explained my approximate analysis of the terms earlier. The kind of continuity that is required (for that to be a change) is part of my intuitive grasp of the term, and while fuzzy, it’s clear enough to guarantee the result.However, assuming for the sake of the argument that I’m mistaken in my analysis of the meaning of the terms, I would withdraw the claim that it is metaphysically impossible that a person transforms into (or becomes) the empty set.
I would not conclude it’s possible, either, since on this assumption for the sake of the argument, I would reckon that I don’t grasp the terms in question well enough to make an assessment.

For my part, the term ‘extended’ is primitive, and I take myself to know its meaning as a result of acquaintance with extended things.

Okay, so I would ask you for a few (not many, just a few) examples of extended things (existent or hypothetical), and a few examples of non-extended things, so that I can try to learn the term as you understand it (that’s not ‘can’ of metaphysical possibility; usually, I don’t use ‘can’ in that sense).
Or maybe the following are correct?
Extended: planets, stars, elephants, and generally anything with surface, volume, etc.
Non-extended: volumeless particles if there are any, souls if there are any, etc.?
Even then, a few more examples of ‘non-extended’ would probably increase precision.

Â ‘Simple’ gets defined in terms of ‘part’, where ‘part’ is primitive.Â

Okay, but that results in fuzziness in my assessment, since it seems to me that’s a matter of how one chooses to categorize things, and while most humans will categorize similarly in most cases, when it comes to weird scenarios, that may well not hold.

I confess I would be very surprised if all the debates in contemporary metaphysics over alleged necessary truths merely turned on a confusion of terms. But of course, I am an “insider” (metaphysics is my area of specialization); so I am certainly biased. 🙂

More than confusion of terms (though imho there is a lot of that going on), many cases seem to be cases of imprecision of terms, and terms that different people use slightly differently, with differences that do not show in ordinary talk (human brains are similar enough), but may well show when things are pushed to borderline cases, as in a number of philosophical discussions.
However, it seems plausible to me that even the above would not cover all of the debates, and I don’t know whether most of them (it may well be that it doesn’t), because:
a. What may well be at play in a lot of cases is diverging intuitive probabilistic assessments about empirical matters where non-transparent rigid designators play a role.
b. There are also implicit probabilistic assessments about strictly logical matters.
As an example of a, let’s say that Bob is assigning (based on a number of other beliefs, including data, etc.) a probability close to 1 to “Water is H2O2”, Alice is assigning close to 1 to “Water is H2O”, Joe is assigning close to 1 to “Water is H2SO4”, and so on.
Of course, in practice matters are a lot more complicated, since the intuitive assessments are made unconsciously and about many, many things.
As an example of b., one may accept that, say, ZFC set theory is almost certainly consistent. That’s a probabilistic assessment: if there were an inconsistency, it would very probably have been found by now. Intuitively, one makes different assessments in some other cases (e.g., one may well be much less willing to say that Goldbach’s Conjecture follows from axioms because no one has found a contradiction if it’s added to them; I think that’s a reasonable assessment).
The issue here is that there might be differences in probabilistic assessments about consistency, etc., resulting perhaps from considering different cases, etc.
When there are so many beliefs and issues involved, it’s very difficult to tell whether the mistakes (and all philosophical views on the issues in question, except for at most one, contain mistakes, often crucial ones) result from something like a, or from something like b., from different people grasping the meaning of a fuzzy term somewhat differently, from logical errors, etc.

To avoid (solve?) sorites puzzles, perhaps.

I’m not tracking you here.
My reply to the sorites issue is based on language imprecision (which is pretty much everywhere (or almost so) in the terms we colloquially use to describe the world around us); others disagree, but I’m not sure what kind of method you’re proposing, and which is not (directly or indirectly) based on logic and meaning of the terms (including rigid designators).
Maybe an example of application that is generally accepted would help me understand what you’re getting at.

Hmmm, you mean like inference to the best explanation, a priori intuition, theoretical cost counting, etc.?

The first one seems like a case of probabilistic assessment, but doesn’t seem to be apart from the kind of methods I mentioned above. But if you have some specific counter-examples (which are generally accepted), I’d like to know about them.
The second (i.e., a priori intuition) is based on one’s grasp of the terms (+ logic, etc.), as far as I can tell. But if you’re thinking of another application of a priori intuitions, as before an example would help.
The third (theoretical cost counting) also seems to be a probabilistic assessment, but I’m not sure in which context that method is applied in a generally accepted manner that is different from the ways I mentioned. An example (in an accepted case) would be good.
But maybe we can simplify:
Do you know of one example of a claim of metaphysical necessity or impossibility that has been accepted after argued for by means of a method that goes beyond logic and meaning of terms (including rigid designators)?

All that makes good sense, Angra.
I suppose much turns on how one understands the meanings of terms in particular cases.
I think your examples of extended and non-extended things are good (though I probably wouldn’t include souls on the non-extended list). To add one more entry to the non-extended list, take numbers, if there are any.Do you know of one example of a claim of metaphysical necessity or impossibility that has been accepted after argued for by means of a method that goes beyond logic and meaning of terms (including rigid designators)
Well, I have a friend who has accepted on the basis of a sorites type argument that it is impossible for anything to have a proper part. His thinking is basically that some objects intuitively don’t jointly compose anything (such as my nose plus the Eiffel Tower). But there is no non-arbitrary division (relevant to mereology) between those cases and the rest; hence nothing has proper parts–and since the reasoning is the same for any possible world, it’s impossible that anything has parts. I’m over-simplifying, of course: he wasn’t persuaded in a day. But over time, he found mereological nihilism to make the best sense of his intuitions. He would deny, however, that this view can be extracted from the definitions of terms, rigid designation, or proof by contradiction. Of course, the sorites arguments that persuaded him is deeply controversial. Different people weigh the considerations differently (and are aware of different considerations). (BTW: he isn’t me.)

I think your examples of extended and non-extended things are good (though I probably wouldn’t include souls on the non-extended list). To add one more entry to the non-extended list, take numbers, if there are any.

Thanks for the information.
That makes me think that maybe we’re actually using different concepts of ‘extended things’, by the way, given that you wouldn’t include souls…then again, maybe we have different concepts of ‘souls’.
Additionally, I’m thinking that the concept of ‘simple’ we’re using may be different. I would consider for instance that if God exist, we can divide his mind in different parts, given that he has many different beliefs, etc., but that’s not what many theists seem to mean by ‘part’.
Now, in daily life, that’s not a problem. We can properly communicate and talk about the parts of whatever we want to talk about (even different parts of a person’s mind), and that works just fine. But when it comes to metaphysical discussions, the difference may be relevant.
It seems to me that that lack of precision and/or knowledge on my part about those particular terms prevents me from properly assessing, at this point, the claim that it’s impossible that there is some X such that X is simple and X is extended, in the senses of ‘extended’ and ‘simple’ in which you’re using the words.
So, I would not take a stance.
Side note: Regarding numbers, I would say that there are, say, infinitely many prime numbers (for example)…in the set of natural numbers. There aren’t any in the empty set. Now, if the claim is that somehow there are numbers ‘out there’, I would not accept the claim. But I’m leaving that aside for the sake of brevity, and since addressing the question of numbers isn’t needed for the considerations above.

Well, I have a friend who has accepted on the basis of a sorites type argument that it is impossible for anything to have a proper part

Thanks for that as well, and sorry, my bad. I meant to say ask for an example of a claimÂ of metaphysical necessity or impossibility that has been generally accepted (i.e., to the point of its being considered non-controversial) after argued for by means of a method that goes beyond logic and meaning of terms (including rigid designators).
Still, the example is interesting (to me), so my take on the sorites argument in question would be:

His thinking is basically that some objects intuitively don’t jointly compose anything (such as my nose plus the Eiffel Tower).Â

I would say that we’re intuitively prone to divide the world we experience in different ways (which we call ‘different objects’), and we tend to consider them independently of each other in a number of ways, even though where we make the divisions seems to be a usually resulting from our psychological predispositions than anything else.
However, stipulating that an object under consideration is composed of your nose and the Eiffel Tower might not be against common meaning of the words, even if it would clearly be very much against common choices of objects, and it would be very inefficient to try to make predictions based on such a division.
On the other hand, I guess it might argued be that the selection of (your nose + the Eiffel Tower) as an object is in conflict with the meaning of the word ‘object’. I think it’s more plausible that there are different ways in which the word ‘object’ is used, depending on context, including one or some that restrict objects to divisions that are more or less intuitive to humans, and one or some that allow for more leeway.

But there is no non-arbitrary division (relevant to mereology) between those cases and the rest; hence nothing has proper parts–and since the reasoning is the same for any possible world, it’s impossibleÂ that anything has parts. I’m over-simplifying, of course: he wasn’t persuaded in a day. But over time, he found mereological nihilism to make the best sense of his intuitions. He would deny, however, that this view can be extracted from the definitions of terms, rigid designation, or proof by contradiction. Of course, the sorites arguments that persuaded him is deeply controversial. Different people weigh the considerations differently (and are aware of different considerations). (BTW: he isn’t me.)

If mereology is meant to reflect at least one (if there is more than one) common meaning of the word ‘part’, and the same goes for ‘object’, I would suggest that the conclusion is not correct.
In particular, I would suggest that ordinarily, we may talk about parts of the human heart, or the human kidney, the parts of a puzzle, or (say), different parts of a car, and those statements are not false.
Also, the divisions make sense for the purposes of study them, understanding them, etc.; it’s not arbitrary like, say, considering the steering wheel and one of the doors of a car as an object (or your nose plus the Eiffel Tower). That would be very impractical.
On the other hand, if mereology is not meant to reflect common usage, then I would need to ask for more information about his usage of the words ‘parts’ and ‘mereology’…
I’m not sure I’m being clear here. Perhaps, the following analogy would clarify my take on this matter.
Let’s consider the case of color.
It seems to me that an object that does not emit light on its own is, say, green, if under certain conditions, it reflects (or rather, would reflect) light in some specific wavelengths; something similar may be said for objects that emit light.
However, how we picked color terms that classify the world around us in a way that tracks those particular wavelengths is of course the result of the fact that we have a certain human visual system, and even further, that some of the divisions that were more relevant to some of our ancestors in certain situations.
As a result, there are some commonalities between color words in different languages, but also clear differences, though actual perception differs considerably less than language it seems.
On the other hand, another intelligent species on another planet, with the capacity to talk but with very different visual systems would surely classify the world around them in a way that is significantly different from the way any humans in any society divide it by color; even if those aliens have something akin to color, it would be associated with other wavelengths.
But that does not mean (in my assessment) that nihilism about color is true, since color terms do not seem to include any ontological commitments to, say, claims about exobiology that turn out
In the case of objects and parts, it may be that (at least in some usages), the distinctions are also based on human normal perception. But in other usages, there may be more leeway in the way we define objects and parts. As long as there is clear and successful communication of information between people using those words (as is usually the case with color talk, part talk, object talk, etc., at least in ordinary speech), then I do not see any good reason to adopt a nihilist theory about them, since there appears to be nothing in the way people are using words (as far as I can tell) that includes ontological commitments that aren’t true.
To be clear, the analogy was an example that I think might explain my take on the matter better, but I’m not making a claim that aliens would probably be as different from us when it comes to parts as they would be when it comes to color (though I think even if they were, that would not be a problem for ordinary talk about parts, so no nihilism would follow).

Thanks Angra,
A few notes, in case they could interest you:
1. By ‘soul’ I mean a fundamentally mental substance that can exist without a body.
2. I agree with what you say about dividing God’s mind into parts. 🙂
3. We may stipulate a meaning for ‘object’ so that the term ranges over all things whatsoever (widest domain of quantification). And let ‘part’ mean whatever it means in normal use (as you suggest). These definitions haven’t resolved the debate among metaphysicians.
4. I am not a nihilist — so I side with you on that. But after sustained discussions on these matters for years with different people, I confess that I find it implausible (though do not rule it out) that the dispute is ultimately over how to define terms. Even after we get reasonably clear on the definitions, there is still disagreement. And in my experience, changes of view on these matters happen not as a result of more careful definitions but as a result of further investigation into the arguments, theoretical costs, etc. That’s my perspective as a metaphysician, anyway. These are deep and difficult waters, of course.

Angra,
I’m curious what you think about Godel’s incompleteness theorems. In particular, I am curious what you make of the proposal that there are well-formed sentences in the language of number theory that are true but not deducible from the axioms. More generally, for any finite set of axioms in the language of number theory, there are true statements not deducible from those axioms. Why wouldn’t such true statements count as necessary truths whose necessity isn’t deducible by your criteria? (What’s deducible is just that there are such un-deducible statements.)

Joshua,
1. Thanks. The issue is now whether ‘mental substance’ is precise enough, and also ‘extended’. So, it’s still a matter of (im)precision as far as I can tell. I’m not sure what else the discussion would be about here. Maybe you have a more precise example of a disagreement on the issue?
2. Great, there is agreement! 😉
3. Okay, by that stipulation, then (your nose + the Eiffel Tower) is clearly an object. So, it does have parts, it seems to me, like the parts of the Eiffel Tower. But if someone disagrees with that, then that would seem to reveal that the normal use of ‘part’ is simply not precise enough to handle cases like that.
On that note, I don’t think that the normal use of most words is exactly the same in all competent speakers, or even precise enough so that a single speaker would at any time make the same assessment in borderline cases (and if that’s what’s going on in the ‘part’ case, I would say that there is no objective fact of the matter as to whether it’s a part, in the colloquial sense of ‘objective fact of the matter’, which I don’t believe is about mind-independence of properties, but in any case).
For example, let’s consider elephants.
Usually, there is an objective fact of the matter as to whether an object is an elephant, whether there are elephants at some time t, etc.
But let’s start at some time t(0) one billion years ago, and let t(n) be t(0) + n yoctoseconds, and let’s consider the statements ‘At t(n), there exists at least one elephant on Earth’.
Is there always an objective fact of the matter as to whether there is an elephant?
It seems to me that that’s not so. The term ‘elephant’ isn’t precise enough. Some competent users of that term would probably be willing to call some objects ‘elephant’, and others would not, even when they’re given all the information they may want about the object in question (though they might change their usage when given information about what others say, but that’s redefining words to resolve communication difficulties).
I don’t see that as an ontological problem, though, but a matter of human psychology and human language. Human minds are very similar to each other, but not exactly the same, so it’s not surprising that the grasp of the meaning of a term based on acquaintance with some (very similar, or even if the same) paradigmatic cases is extremely similar but not exactly the same across speakers, for many terms, and I’d say most terms at least.
4.

Â Even after we get reasonably clear on the definitions, there is still disagreement.

A couple of points:
1. Definitions are only as clear as the terms used in them; point 3 above is an example; alternatively, one may consider the disputes over whether Pluto was a planet. It wasn’t a dispute about anything regarding Pluto’s mass, size, orbit, etc., rather, different people seemed to be using the word ‘planet’ differently; the differences did not have an impact in most cases (e.g., the Earth, Mars, etc., would be planets under anyone’s concept), but it did with Pluto.
Perhaps, the Pluto example is not the best because there were emotional issues at play too, which obscure the matter a little, but the idea it pretty much that.
2. Conceptual analysis is often difficult even when different parties are using the words in a significantly similar manner, because there might be aspects of the scenario under consideration that different people may be failing to picture, factor in, etc., and which would yield a different result (different from the position they’re defending at a particular moment), if they were to consider them.

And in my experience, changes of view on these matters happen not as a result of more careful definitions but as a result of further investigation into the arguments, theoretical costs, etc. That’s my perspective as a metaphysician, anyway.

Thanks for your input.
Not being a metaphysician, I have to admit I don’t have nearly as much experience to assess the matter.
That said, what you mention above (further investigation, theoretical costs) does not seem to be in conflict with my take on this.
For instance, in the case of further investigation of the arguments, it may well be that the meaning of a term across philosophers is similar enough to yield a unique result on the matter under analysis, but it turns out that some philosophers have not yet considered some of the details of what is being described, and based on that, they’re mistaken about it.
In the case of theoretical costs, also it seems to me in some cases they’re checking whether accepting some views yields results that contradict the common usage of the terms; some other times, maybe a colloquial word is not precise enough for some philosophical usage, and what some philosophers are doing by taking a stance is actually extending those terms to the previously borderline cases, with more precision, in a way that would be useful for communication using those terms, etc.
That said, it’s true that you have many more examples of that, so I may very well be missing something here. Perhaps, an example would help, but I would need a certain amount of detail about how someone was persuaded, etc., so maybe that would take too long, I’m not sure.
In any case, and to clarify my view I’m not saying that it’s usually the case that different philosophers are using the words differently, by the way. As I mentioned in an earlier post, there are a number of other ways in which they might end up having different views (e.g., see the ‘Water is H2O2″ cases, the example involving axioms, etc.).

These are deep and difficult waters, of course.

Yep, I agree.

I’m curious what you think about Godel’s incompleteness theorems. In particular, I am curious what you make of the proposal that there are well-formed sentences in the language of number theory that are true but not deducible from the axioms. More generally, for any finite set of axioms in the language of number theory, there are true statements not deducible from those axioms. Why wouldn’t such true statements count as necessary truths whose necessity isn’t deducible by your criteria? (What’s deducible is just that there are such un-deducible statements.)

Nitpicking: If you pick inconsistent axioms, you may derive anything. 😉
But that’s a very interesting (and complicated) matter.
I don’t have the time to write a proper explanation of my take on it at the moment, so I’ll have to leave it for later (but it will be along the lines of what one means by ‘natural numbers’; the same goes for sets, etc.).

All of that makes sense, Angra. Yeah, certainly there are different possible stories about why disagreement among philosophers persists even after much effort has been made to get definitions clear. Just to illustrate how entrenched the debates are, some philosophers will insist that there is no possible meaningful sense of the term ‘object’ on which some object has parts (on the normal sense of ‘part’), though intuitions may strongly tempt us to think otherwise. Of course, a story is possible: maybe they still aren’t really working with the same concept of ‘object’, etc.
Here is another issue to think about, which comes from E.J. Lowe: Let X = âThe proposition that it is not the case both that Ferdy is a female fox and that Ferdy is not a female fox is an instance of the logical law that for any proposition P, it is not the case both that P and not-Pâ Lowe says that X is necessary but not strictly logically necessary (since it is neither a logical law nor deducible from one). Maybe you’ll say this gets resolved by rigid designation.
As for the Godel case, you might let all the unprovable truths be part of an implicit definition of ‘natural numbers’. Then the definition will have infinite conceptual complexity, though that doesn’t seem right to me.
Going back to the original topic, I think I would agree with you that the GR argument doesn’t give a good reason to think that an infinity of past events is impossible by your criteria of impossibility. In fact, this might be a good example of a dispute that really does just turn on a semantic difference (in which case there was no real ontological dispute–which I don’t mind. 🙂 And recognizing this is a form of progress.)
I think the whole GR argument discussion is helpfully prefaced with a comment about the role and meaning of ‘broad logical possibility’ in its formulation. Thanks to you for helping to bring this issue to the forefront.

Just to illustrate how entrenched the debates are, some philosophers will insist that there is no possible meaningful sense of the term ‘object’ on which some object has parts (on the normal sense of ‘part’), though intuitions may strongly tempt us to think otherwise. Of course, a story is possible: maybe they still aren’t really working with the same concept of ‘object’, etc.

We may sidestep the issue of ‘object’ and consider only claims about parts.
For instance, would those philosophers say that when people talk about the parts of a car, of the heart, the liver, of the parts of a cell phone, etc., they’re making false statements all the time?
If so (which is the impression I get from your post), I would disagree, but I would say that the matter is about the meaning of the term ‘parts’, and in particular about the ontological commitments of claims about parts, and on whether saying, say, “The parts of the heart are such-and-such” always entails some false ontological claims.
While I guess they might be using a very different concept of ‘parts’ from the rest of us, they might have made a mistake due to some other false philosophical theory they believe in; I tend to think this is more probable, but I recognize that I might be wrong (in any case, it still seems to be about the meaning of ‘parts’).

Here is another issue to think about, which comes from E.J. Lowe: Let X = âThe proposition that it is not the case both that Ferdy is a female fox and that Ferdy is not a female fox is an instance of the logical law that for any proposition P, it is not the case both that P and not-Pâ Lowe says that X is necessary but not strictly logically necessary (since it is neither a logical law nor deducible from one). Maybe you’ll say this gets resolved by rigid designation.

I’d say meaning of the words, (like ‘All bachelors are unmarried’, or perhaps even better, ‘If Bob is a bachelor, then he is not married’, etc.), once one considers the meaning of ‘logical law that for any proposition…’, etc.

As for the Godel case, you might let all the unprovable truths be part of an implicit definition of ‘natural numbers’. Then the definition will have infinite conceptual complexity, though that doesn’t seem right to me.

I’m planning to write a reply as soon as I can.
Just a question: is it okay if I switch to set theory instead?
The reason is that it seems to me I would be able to address the same issue you’re apparently trying to get at (i.e., there are formulas such that neither them nor their negation follows from the axioms, and then what happens to truth in that context), while saving time by not getting into some of the details of Godel’s proof (even similar simplified proof have that difficulty).
The matter is very interesting, but I’m afraid it’s already taking a bit too long, and meatspace sometimes gets in the way (on that note, I’m afraid I’m going to step out of this and the other thread by the end of the week:( ) , so I wouldn’t want to start on Godel if I’m then not able to explain my view sufficiently clearly.
Still, if you think the set theory case is relevantly different, I’ll try to come up with an explanation on the natural numbers case without making it too long.
On the GR issue, you’re welcome, and thank you for your thoughts too.

Cool observations. Some further thoughts:
1. I know it may seem crazy, but the philosophers I have in mind would say that when people talk about the parts of a car (in the ordinary sense of ‘part’), they speak falsely. These philosophers usually try to give a story as to why our intuitions about parts and wholes mislead us.
2. There’s no need to get bogged down with detailed response to the Godel case. I’m sure you could convey what you have in mind, if you wish, with a general gesture.
3. I wonder if significant progress could be made by more explicitly defining the terms used in the criteria you have in mind. I say this because I am unsure how those terms are to be defined without making use of a primitive notion of ‘possibility’ (or ‘necessity’). Take, for example, ‘x is a rigid designator’. What do you mean by that? Or ‘x is strictly logically necessary’. My math professor friend once gave me a detailed definition of ‘x is strictly logically necessary’ that eliminated modal expression like ‘is possibly deduced’, but the result was a definition that implied that there are unexpressed propositions, and I take it that your nominalist ontology commits you to rejecting the existence of unexpressed propositions.
Another expression that may show up in your criteria (depending upon how it is explicitly defined) is ‘can tell a priori by the meaning of terms’.
4. Here is a classic example of a sentence whose necessity seems to me to be broadly logically necessary: ‘for any x, if every part of x is red, then no part of x is blue’. I suspect you’ll say that its necessity can be deduced from your criteria. Maybe an explicit definition of your criteria would help me see how. Alternatively, maybe your effort at explicitly defining the terms of your criteria could lead to further discoveries for both of us. 🙂
5. We’ll have to move swiftly to bring resolution by your deadline. I remain optimistic. 🙂

Joshua,
1. It’s okay, I’m used to running into views that I find extremely improbable. 🙂
Anyway, as I said I disagree with their views, but the disagreement seems to be clearly about the meaning of the words, since they believe that the sentence (in the usual sense) ‘the parts of a car are such-and-such’ (for instance) makes an ontological claim about things that do not actually exist, whereas I disagree, since I don’t see any good reason to believe that.
2. You’re giving me too much credit, but I’ll try.
For instance, let’s say that I have an intuitive concept of ‘set’, and also ‘hereditary set’. How I came to have concepts is an interesting matter on its own, but not what I’m trying to get at (very briefly and very sketchily, I’d say that given our experience and our innate cognitive traits, humans intuitively make abstractions from observing groups of things and come up with sets, numbers, etc.; other humans just learn from other humans before them, etc.).
So, in order to reduce the chances of paradoxes, I want a system of axioms to develop a theory about hereditary sets (also, the motivation for that are another matter, but that would that a bit long).
Assuming I’m a smarter and spend a lot of time, etc., I come up with axioms like existence of empty set, axiom of infinity, power set, etc.
Now, to be clear, when I say that there is an empty set, I’m not making an ontological claim like saying that there are planets other than Earth orbiting the Sun.
The claim may be understood as a claim that in a scenario, category or class (pick your word) that contains all of the (hypothetical) objects that meet the conceptual conditions to be a hereditary set, there is one that is the empty set, and is unique because set identity is given by membership (also, a. conceptual matter).
Now, that I come up with some axioms does not mean that I’ve identified all of the truths about hereditary set. For instance, many of those truths follow from the axioms. Others do not, and would require more axioms.
Moreover, just as when we come up with hypothetical scenarios involving people, the scenarios are not complete (perhaps, we should call them ‘categories of scenarios’), in the case of hereditary sets, it may well be (I would say it is so) that my concept of ‘hereditary set’ does not provide enough conditions to fully determine the scenario.
Also, there probably are some differences between the intuitive understanding of ‘hereditary set’ which I would use, and the intuitive concept other people would use, and generally the concept varies to some extent.
When that happens, I don’t think there is any reason for disagreement. We may as well consider different axiom systems and their consequences, and some of those systems would be more precise reflections of the intuitive concept some people have, and others might be more precise reflections of the intuitive concepts others have.
Also, there are cases (e.g., some cases of rejection of the axioms of choice or infinity) in which the motivation for the rejection is not a different intuitive concept of ‘hereditary set’, but a mistake resulting from some false philosophical view that for some reason or another a person ended up holding.
But in any event, we may consider the axioms directly, and the objects would be something like ‘whatever matches the axioms’.
So, is the axiom of choice necessarily true?
If by ‘hereditary set’ we mean what I intuitively understand by that, yes.
So, if HSAM rigidly designates my concept of hereditary set, then for every HSAM of non-empty HSAM, there is a choice HSAM. That’s necessary because it can be establish by my concept of hereditary set (or, if you like and from a somewhat different but I think equivalent perspective, the scenario, class or category ‘hereditary sets’ I intuitively construct is such that it contains elements like that)
But perhaps someone has a different concept (i.e., not one of the errors I mentioned above), and does not include AC. No problem. We may consider different axioms and their consequences. It’s just that some axiom systems will be perhaps more suited to describe a category, scenario, etc., that is intuitive to one person, and others will work better for another person. Even so, there is a lot of similarity given the similarities of human minds, so the systems will not be (usually) radically different.
Moreover, sometimes we start the other way: we may learn the axioms first, and then grasp an intuitive concept of any objects such that the category of all such objects is a model for the axioms (i.e., they’re true of that category, scenario or whatever one calls it). And in that way, some areas of mathematics may develop far beyond the original concepts that we got from observations and abstraction.
But I don’t see anything problematic here (very difficult, sure, but I mean not that I would find a problem for my views on any of these matters, or for what I propose about metaphysical possibility).
Back to the natural numbers, the intuitive concepts of ‘natural number’ and the corresponding category ‘natural numbers’ of all of the objects (hypothetical, etc.) that meet the criterion for being a natural number (identified up to number isomorphism, which is also given by the concept of ‘natural number’ in question) is such that if we come up with a recursively enumerable set of axioms, there will be truths about natural numbers that won’t follow from them.
But that’s not really a problem, as far as I can tell. The concept comes first, the axiomatic system later. If no axiomatic system (recursive, etc.) entails all truths about it, then so be it. The truths are still necessary, and we may even some of them to the axioms (clearly, there will still be others that don’t follow from the new axioms, if the system is recursive), though usually that’s not needed for studying the properties of natural numbers that we (for different reasons) care about.
3. Unfortunately, we need to leave some terms undefined always. But you seem to be taking metaphysical possibility, necessity, etc., as primitive. I’m not sure that that would be the case. It seems to me that the primitive concept would be something like strict logical possibility and meaning, etc…though actually, maybe the concept of truth is more primitive and may be used.
In any case, some of the terms will be undefined.
Regarding ‘x is strictly logically necessary’, one may offer a definition for first-order formulas, and then for sentences in a natural language, if they’re expressed by substituting terms in one such formula. As for propositions, as long as they’re expressed (potentially) by some sentence in some language, then the same would apply, or have structure.
Regarding your point about unexpressed propositions, just as I may consider a category ‘hereditary sets’ of all objects meeting some conditions, I may do the same for propositions, so whether someone has expressed them is not the difficulty. The difficulty, rather, is grasping the concept ‘proposition’ in a way that is separated from any structure, or terms, etc..
For instance, perhaps, very tentatively I would suggest the following preliminary approximation:
A proposition is strictly logically necessary if one there are propositions P1, P2,..; Pn, and a strictly logically necessary formula such that P is the proposition A(P1,P2,…;Pn)
Maybe one would need extensions for the definition of strictly logically necessary formulas in higher order logic, and perhaps for infinite cases and maybe iterations (like that P), but the idea would be like that.
On the other hand, if that fails too and the proposed propositions do not need to have structure, maybe an alternative is to say that a proposition is strictly logically necessary if its negation is a contradiction, and leave ‘contradiction’ as primitive (I’m not sure that captures the exact meaning, but it’s at least equivalent it seems to me).
4. I’m afraid I don’t know how to define those terms, and I suspect that those are primitive. Maybe we’re using different primitive terms?
But let’s consider your sentence:

I suspect you’ll say that its necessity can be deduced from your criteria.

The proposal I gave in terms of contradictions seems to match the meaning of ‘metaphysically impossible’, as I understand it. When it comes to ‘metaphysically necessary’, the basic concept may not be in terms of negations of impossibilities, though I’m not entirely sure.
Still, as you correctly suspected :), I do say that the necessity of the proposition you bring up can be deduced from my criteria.

Maybe an explicit definition of your criteria would help me see how.

Trying to match the meaning for necessity is difficult (we’re still working on strict logical necessity, which I would have considered primitive), so I would go with the indirect criteria I offered before (since it’s clear by the way people use the words that the negation of a necessity is an impossibility, so checking for impossibilities works).
So, formalizing the sentence (at least, that’s how I understand it; please let me know if I missed something):
R(x) means ‘x is red’.
B(x) means ‘x is blue’.
P(y,x) means ‘y is a part of x’.
Ax means ‘for all x’.
Ex means ‘there exists some x’.
The sentence would be:
RB: Ax(Ay(P(y,x)âR(y))âÂ¬Ez(P(z,x)&B(z)))
Given the concepts of ‘blue’ and ‘red’, I would say that “All things that are red are not blue” is like “All bachelors are unmarried”, so that one counts by my criteria as necessary (If it’s red and blue (e.g., half and half), it does not count as red, or blue. I’m considering all red and all blue only since that is what you seem to mean in context; otherwise, the claim about the parts is not necessarily true, because a part could be half red and half blue, etc.).
So, the proof of a contradiction:
L1. Ax(R(x)âÂ¬B(x))
L2. Â¬RB: Â¬Ax(Ay(P(y,x)âR(x))âÂ¬Ez(P(z,x)&B(z)))
L3. ExÂ¬(Ay(P(y,x)âR(y))âÂ¬Ez(P(z,x)&B(z))) [From L2, using logically necessary formulas; the entire first order derivation would take long, but one can get it from the axioms]
L4. Ex(Ay(P(y,x)âR(y))&Ez(P(z,x)&B(z))
L5. Ex(Â¬EyÂ¬(P(y,x)âR(y))&Ez(P(z,x)&B(z)) [From L3, using logically necessary formulas]
L6- Ex(Â¬Ez(P(z,x)&Â¬R(z))&Ez(P(z,x)&B(z)) [from L5, using logically necessary formulas and substituting bounded variables].
L7. Ex(Â¬Ez(P(z,x)&Â¬R(z))&Ez(P(z,x)&Â¬R(z)) [from L6 and L1, using logically necessary formulas]
L8. Ex(Â¬F(x)&F(x)) [renaming, where F(x) means Ez(P(z,x)&Â¬R(z))].
L9. Â¬Ax(F(x)vÂ¬F(x) [from 8, using logically necessary formulas]
L10. Ax(F(x)vÂ¬F(x) [logically necessary formula]
L11. A contradiction follows from 9 and 10.
5. I think we’ve addressed a number of points already, so even if there is no further resolution, it’s been a very interesting discussion. 🙂

Angra, thanks. Some further thoughts:
1. My point is just that the disagreement isn’t merely about words, since even after the meanings of the terms are fixed and reasonably clear, there is still a disagreement over the truth of the proposition expressed (it appears to me).
2. I happily disagree about giving you too much credit; you deserve far more! Thanks for your comments about axioms, etc., which make sense (and inspire further issues, which I am content to leave to the side).
3. For what it is worth, I do not myself recognize a distinction between the meaning of ‘there is an x, such that …’ and ‘there is *really* (ontologically) an x, such that’. (Btw: I translate fictional talk into talk about stories, which I take to exist.)
4. Impressive proof. I take the very first step to be the most critical: Ax(R(x)âÂ¬B(x)), which reads “whatever is [all] red is not [all] blue”. This statement is among the very things I take to be unprovable just by extracting the meanings of terms. Now one might think ‘not blue’ is part of the meaning of ‘red’, since redness is not blueness. But consider that redness is not triangularity, yet there could be an all red thing that *is* triangular. Also, suppose ‘not blue’ is included in the meaning of the term ‘red’. Then by the same reasoning, it would seem that ‘not red’ should be included in the meaning of the term ‘blue’. But that leads to a regress of inclusions: ‘red’ means ‘not not …’. Or we get circularity: ‘red’ means ‘not not … red’.
I think what may be going on here is that you “see” a priori that whatever is all red isn’t also all blue, and that you see this when you grasp the proposition expressed by words whose meanings you understand. So, you say “it is true by the meanings of the words”. In the case of ‘all bachelors are unmarried’, I think there is an importantly different, more narrow sense in which the claim is true by the meanings of the words, since ‘unmarried’ is part of the meaning of ‘bachelar’ (whereas ‘not blue’ is not part of the meaning of ‘red’, else the regress problem).
So, perhaps we can make progress by recognizing a distinction: ‘True by the meaning of the words’ has a narrow sense and a broad sense. Taken broadly, your criteria comes close to capturing what I have in mind when thinking of metaphysical impossibility (depending upon what goes into the notion of ‘rigid designation’). Taken narrowly, I suspect–hope–we can agree that ‘whatever is all red is not all blue’ isn’t true by the meaning of the words.
5. The exchange has been a pleasure, as usual.

Joshua,
I’m having computer problems, so I’ve not been able to log in.
1. But it seems to me that the disagreement is about what the proposition expressed by a sentence is.
For example, letâs consider the sentence âThe doors are some of the parts of a carâ.
Letâs say that Philosopher 1 says itâs true, but Philosopher 2 says itâs false.
It seems to me that they do not disagree (normally) about whether or not there are cars that have doors. They both agree (I hope). Also, they do not disagree about any property of the car or the doors like size, mass, color, etc. (or so I hope, also, but letâs say that they donât disagree, to isolate the specific disagreement about parts).
Yet, they disagree about whether the sentence is true. The reason seems to be that Philosopher 2 believes that the meaning of the words is such that the sentence makes some ontological claim O1, which is false, and Philosopher 1 does not believe that any such claim is being made (she believes it isnât).
But then, letâs consider the proposition expressed by the sentence. It seems to me that given their disagreement about the meaning of the words, they disagree about what the proposition is.
As I see it, Philosopher 1 may well agree that the proposition that Philosopher 2 claims is expressed by the sentence, is false. However, Philosopher 1 believes thatâs not what the sentence expresses.
Now, that does not mean that Philosopher 1 and Philosopher 2 have such a different concept of âpartsâ that an error theory holds for Philosopher 2 talk of parts, but not for Philosopher 1 talk of parts.
It may well be that Philosopher 2 has made a mistake in her conceptual analysis of âpartsâ, and so even though she may well make true assertions involving parts, she does not realize that those assertions would be true (that might sound odd, but we wouldnât expect that moral assessments like âX is immoralâ made by moral error theorists are all false, so Iâm not sure part error theorists make false statements about parts).
Still, it might be that Philosopher 2 refrains from making any claims about parts, but even then, she intuitively does grasp the usual meaning of the terms, and is able to normally understand true claims about parts made by other people (just as moral error theorists do understand moral assessments, on an intuitive level).
Then again, perhaps Philosopher 2, for one reason or another, ended up with a concept of âpartsâ under which nothing has parts. In any case, the disagreement seems to be about what the common concept (or concepts) is.
Other than that, I donât see what the disagreement might be about, at least in that case (i.e., parts).
To be clear, Iâm talking about the case of parts.
There are other cases in which the disagreement is not about the meaning of the words, but about some ontological matter picked by rigid designators (or something kind of like that), etc.; moreover, there may be disagreement between several different options, and some of the disagreement is about the meaning of the words, whereas some of the disagreement is about whether something the words (they agree) try to pick or track, actually exists.
For instance, letâs say that Philosopher 3…or Bob, to make it simpler, believes that unless God exists (for some definition of âGodâ), there are no moral obligations because moral terms are such that propositions asserting that people have obligations entail propositions about God, and he also believes God does not exist, and there are no moral obligations.
Alice, on the other hand, agrees that God does not exist, but does not believe that moral terms are such that moral assessments like âTom behaved immorally when he cheated on his wife for funâ entail propositions about any kind of non-human agent, or any other thing that is actually false (depending on the case, of course, sometimes the moral assessment is false for some other reason).
Finally, Mary agrees with Bob about the ontological commitments of moral language, but believes that God exists and there are moral obligations.
In that case, Alice and Bob disagree on the meaning of the words, Alice and Mary disagree about both the meaning of the words and the existence of God, whereas Bob and Mary agree about the meaning of the words, but disagree about the existence of God.
So, there are plenty of options. In the case of parts, it seems to me that the disagreement is about the language at least, and also that when it comes to parts of regular, daily life objects, about nothing more, since there is no disagreement about whether there are cars with doors, etc. (again, I hope there isnât, but if there is, Iâd say that probably theyâre also disagreeing about the meaning of the word âcarâ, etc., unless one of the philosophers is a radical skeptic or something like that).
2. Thank you.
3. I donât think that the term âreallyâ is such that âthere is an x, such that…â and âthere really is an x, such that…â, so in that sense, I recognize no such distinction.
On the other hand, I do think that there is a difference between a claim like, say, âThere are infinitely many prime numbers…â, and a claim made by a Platonist philosopher that there are infinitely many prime numbers, in a context of doing metaphysics rather than mathematics, and in which the philosopher in question maintains that we ought to include those numbers in an ontology because (allegedly) they do exist âout thereâ so to speak (in some Platonic realm).
In other words, I donât think that âthere is an x…â, or âthere are infinitely many xâs…â in mathematics is an ontological claim in the sense of ontology in philosophy.
Something like âfor any such-and-such set, there is a choice set…â, or âthere is an empty setâ, etc., seems to mean, in my view (and in ordinary math talk), that there is such set in the category/scenario âhereditary setsâ (whose elements are all hereditary sets), but it does not seem to be a claim like âthere are exoplanets orbiting star Xâ
So, I guess we disagree on that point.
4.

Also, suppose ‘not blue’ is included in the meaning of the term ‘red’. Then by the same reasoning, it would seem that ‘not red’ should be included in the meaning of the term ‘blue’. But that leads to a regress of inclusions: ‘red’ means ‘not not …’. Or we get circularity: ‘red’ means ‘not not … red’.

Itâs not that âredâ means ânot blueâ in the intensional sense, but rather that their meanings make them incompatible, and we can tell that.
For instance, letâs consider the following case:
NTFD: All two-door cars are not four-door cars.
NTFD is true, and we can tell that just by the meaning of the words and logic, but going by something like your argument above, it seems to me that one would have to say that we canât tell that by the meaning of the words and logic alone.
If you think that NTFD is relevantly different from the blue/red case, please let me know why.
Alternatively, if you think we canât decide NTFD by logic and the meaning of the words alone, please let me know as well.
At any rate, and as an alternative in the case of red/blue, I may go with rigid designators too (though that is a roundabout and I would say more problematic way, but still).
So, I would say that an object that does not emit light (similar for those that do) is blue if, under certain conditions, reflects certain and absorbs wavelengths in some specific way. The same for red, only the wavelengths do not match. That would be a rigid designator Iâd say, so I might use that to establish the premise as well, even if with a different reasoning (though of course you might challenge whether thatâs a rigid designator, and that would also be a disagreement about the meaning of the words).

So, perhaps we can make progress by recognizing a distinction: ‘True by the meaning of the words’ has a narrow sense and a broad sense. Taken broadly, your criteria comes close to capturing what I have in mind when thinking of metaphysical impossibility (depending upon what goes into the notion of ‘rigid designation’). Taken narrowly, I suspect–hope–we can agree that ‘whatever is all red is not all blue’ isn’t true by the meaning of the words.

Iâm still trying to grasp the meaning of the ânarrow senseâ meaning of the words, so I will wait for your assessment about the NTFD case, but it may well be we were using âmeaning of the wordsâ differently.
5. Likewise.

Joshua,
1. But it seems to me that the disagreement is about what the proposition expressed by a sentence is.
For example, Wikipedia gives a list of auto parts.
So, letâs consider the sentence âThe doors are some of the parts of a carâ.
Letâs say that Philosopher 1 says itâs true, but Philosopher 2 says itâs false.
It seems to me that they do not disagree (normally) about whether or not there are cars that have doors. They both agree (I hope). Also, they do not disagree about any property of the car or the doors like size, mass, color, etc. (or so I hope, also, but letâs say that they donât disagree, to isolate the specific disagreement about parts).
Yet, they disagree about whether the sentence is true. The reason seems to be that Philosopher 2 believes that the meaning of the words is such that the sentence makes some ontological claim O1, which is false, and Philosopher 1 does not believe that any such claim is being made (she believes it isnât).
But then, letâs consider the proposition expressed by the sentence. It seems to me that given their disagreement about the meaning of the words, they disagree about what the proposition is.
As I see it, Philosopher 1 may well agree that the proposition that Philosopher 2 claims is expressed by the sentence, is false. However, Philosopher 1 believes thatâs not what the sentence expresses.
Now, that does not mean that Philosopher 1 and Philosopher 2 have such a different concept of âpartsâ that an error theory holds for Philosopher 2 talk of parts, but not for Philosopher 1 talk of parts.
It may well be that Philosopher 2 has made a mistake in her conceptual analysis of âpartsâ, and so even though she may well make true assertions involving parts, she does not realize that those assertions would be true (that might sound odd, but we wouldnât expect that moral assessments like âX is immoralâ made by moral error theorists are all false, so Iâm not sure part error theorists make false statements about parts).
Still, it might be that Philosopher 2 refrains from making any claims about parts, but even then, she intuitively does grasp the usual meaning of the terms, and is able to normally understand true claims about parts made by other people (just as moral error theorists do understand moral assessments, on an intuitive level).
Then again, perhaps Philosopher 2, for one reason or another, ended up with a concept of âpartsâ under which nothing has parts. In any case, the disagreement seems to be about what the common concept (or concepts) is.
Other than that, I donât see what the disagreement might be about, at least in that case (i.e., parts).
To be clear, Iâm talking about the case of parts.
There are other cases in which the disagreement is not about the meaning of the words, but about some ontological matter picked by rigid designators (or something kind of like that), etc.; moreover, there may be disagreement between several different options, and some of the disagreement is about the meaning of the words, whereas some of the disagreement is about whether something the words (they agree) try to pick or track, actually exists.
For instance, letâs say that Philosopher 3…or Bob, to make it simpler, believes that unless God exists (for some definition of âGodâ), there are no moral obligations because moral terms are such that propositions asserting that people have obligations entail propositions about God, and he also believes God does not exist, and there are no moral obligations.
Alice, on the other hand, agrees that God does not exist, but does not believe that moral terms are such that moral assessments like âTom behaved immorally when he cheated on his wife for funâ entail propositions about any kind of non-human agent, or any other thing that is actually false (depending on the case, of course, sometimes the moral assessment is false for some other reason).
Finally, Mary agrees with Bob about the ontological commitments of moral language, but believes that God exists and there are moral obligations.
In that case, Alice and Bob disagree on the meaning of the words, Alice and Mary disagree about both the meaning of the words and the existence of God, whereas Bob and Mary agree about the meaning of the words, but disagree about the existence of God.
So, there are plenty of options. In the case of parts, it seems to me that the disagreement is about the language at least, and also that when it comes to parts of regular, daily life objects, about nothing more, since there is no disagreement about whether there are cars with doors, etc. (again, I hope there isnât, but if there is, Iâd say that probably theyâre also disagreeing about the meaning of the word âcarâ, etc., unless one of the philosophers is a radical skeptic or something like that).
2. Thank you.
3. I donât think that the term âreallyâ is such that âthere is an x, such that…â and âthere really is an x, such that…â, so in that sense, I recognize no such distinction.
On the other hand, I do think that there is a difference between a claim like, say, âThere are infinitely many prime numbers…â, and a claim made by a Platonist philosopher that there are infinitely many prime numbers, in a context of doing metaphysics rather than mathematics, and in which the philosopher in question maintains that we ought to include those numbers in an ontology because (allegedly) they do exist âout thereâ so to speak (in some Platonic realm).
In other words, I donât think that âthere is an x…â, or âthere are infinitely many xâs…â in mathematics is an ontological claim in the sense of ontology in philosophy.
Something like âfor any such-and-such set, there is a choice set…â, or âthere is an empty setâ, etc., seems to mean, in my view (and in ordinary math talk), that there is such set in the category/scenario âhereditary setsâ (whose elements are all hereditary sets), but it does not seem to be a claim like âthere are exoplanets orbiting star Xâ
So, I guess we disagree on that point.
4.

Also, suppose ‘not blue’ is included in the meaning of the term ‘red’. Then by the same reasoning, it would seem that ‘not red’ should be included in the meaning of the term ‘blue’. But that leads to a regress of inclusions: ‘red’ means ‘not not …’. Or we get circularity: ‘red’ means ‘not not … red’.

Itâs not that âredâ means ânot blueâ in the intensional sense, but rather that their meanings make them incompatible, and we can tell that.
For instance, letâs consider the following case:
NTFD: All two-door cars are not four-door cars.
NTFD is true, and we can tell that just by the meaning of the words and logic, but going by something like your argument above, it seems to me that one would have to say that we canât tell that by the meaning of the words and logic alone, since ‘two’ does not mean the same as ‘not four’.
If you think that NTFD is relevantly different from the blue/red case, please let me know why.
Alternatively, if you think we canât decide NTFD by logic and the meaning of the words alone, please let me know as well.
At any rate, and as an alternative in the case of red/blue, I may go with rigid designators too (though that is a roundabout and I would say more problematic way, but still).
So, I would say that an object that does not emit light (similar for those that do) is blue if, under certain conditions, reflects certain and absorbs wavelengths in some specific way. The same for red, only the wavelengths do not match. That would be a rigid designator Iâd say, so I might use that to establish the premise as well, even if with a different reasoning (though of course you might challenge whether thatâs a rigid designator, and that would also be a disagreement about the meaning of the words).

So, perhaps we can make progress by recognizing a distinction: ‘True by the meaning of the words’ has a narrow sense and a broad sense. Taken broadly, your criteria comes close to capturing what I have in mind when thinking of metaphysical impossibility (depending upon what goes into the notion of ‘rigid designation’). Taken narrowly, I suspect–hope–we can agree that ‘whatever is all red is not all blue’ isn’t true by the meaning of the words.

That sounds plausible. I will wait for your assessment about the NTFD case to be sure, but it may well be we were using âmeaning of the wordsâ differently.
5. Thanks, and likewise.

Joshua,
A brief comment on 4.
It does look like we were using ‘meaning of the words’ differently, though I’m not sure that in the sense I meant it, that would match your idea of ‘metaphysically impossible’. Maybe it does, though. I’m just not sure, especially given GR arguments and the like.

Thanks Angra,
1. It seems to me that they do not disagree (normally) about whether or not there are cars that have doors. They both agree (I hope) Unfortunately, sometimes they don’t agree even about that, and the reason for the disagreement isn’t, according to them anyway, over what claim the sentence is making. I’m just reporting my own experience with these sorts of conversations.
3. I understand what you are saying; I just don’t see how to carve the distinction you are making, such that there is a meaning of ‘there is’ that isn’t ontologically committing (unless there is a plausible translation).
4. The NTFD case is less clear to me only because it is less clear how ‘number’ is to be defined, but I trust you get the general distinction I was trying to make over the meaning of ‘meaning of terms’, and now the difference between us probably turns on the meaning of ‘rigid designator’ (I suspect).

1.Â It seems to me that they do not disagree (normally) about whether or not there are cars that have doors. They both agree (I hope)Â Unfortunately, sometimes they don’t, and the reason for the disagreement isn’t, according to them, anyway, over what claim the sentence is making. I’m just reporting my own experience with these sorts of conversations.

Some philosophers might be radical skeptics, but at least from what I’ve seen, the disagreement is about what claim the sentence is making, even though in some cases they might disagree with my claim that their disagreement is about the claim the sentence is making. I might be mistaken, of course; also, maybe the cases you’re thinking about are not like the ones I’m thinking about.
But let me try to explain why I think that the issue is with the meaning of the sentence (other than, perhaps, logical errors).
For instance, based on what you say above, it seems that at least one of the philosophers you mention does not believe that there are cars that have doors. Do they disagree that there are cars and doors, or just that cars have doors?
In any case, let’s consider the following sentence S1, in colloquial English, and the proposition it expresses, P1.
S1: At some point in 2002, the Queen of England had a four-door car with a special rear-door mechanism.
Now, I say S1 and P1 are true. In case someone disagrees about sentences and/or propositions, I say that at some point in 2002 the Queen of England had (among other cars, perhaps) a four-door car with a special rear-door mechanism.
But let’s say some of the philosophers you know would disagree with my assessment. Would they:
a. Mistrust the pictures, the reports, etc. (e.g., say that someone made it up).
b. Think that the object the pictures portray fails to meet some criteria for being a four-door car with a special rear-door mechanism.
c. Other.
Case a. seems clearly not the case (if that is the case, then I would have to concede the disagreement is not about the meaning of the words in that particular case.
That isn’t problematic for my general position since I believe that not all disagreements are like that (e.g., my metaethics example), and I don’t know what percentage of them is, but still it would be a curious case.
If it’s case b., it seems to me that the disagreement is almost certainly about the meaning of the sentence (and thus, about the proposition expressed by it), since the criteria in question depend on that meaning, not on something else, as far as I can tell. If you (or they) think otherwise, I’m really curious about it (really, I want to know what this is about; it’s very intriguing).
If it’s c., I would ask for a brief explanation as to why they would deny P1 and/or S1, if that’s feasible.
3. Okay, I just don’t think that the usual ‘there is’ in mathematics is ontologically committing, so it seems to me that we have a disagreement about the meaning of the words.
In this case, this disagreement may well result in a number of ontological disagreements, since it’s clear (to me, and I guess to you?) that the ordinary claim ‘There are infinitely many primes’ is true, so while I wouldn’t include anything in an ontology as a result, you might include infinitely many prime numbers.
4. In NTFD, ‘two-door car’ and ‘four-door car’ are used to mean what those terms colloquially mean.
Even if you think the meaning is unclear, one might reason as you did in the case of blue and red, as follows: Suppose ‘not four’ is included in the meaning of the term ‘two’. Then by the same reasoning, it would seem that ‘not two’ should be included in the meaning of the term ‘four’. But that leads to a regress of inclusions…(unless, perhaps, you think that maybe ‘not two’ is included in the meaning of ‘four’ but not vice versa?).
Still, given your reply, I think I’m getting the distinction you’re trying to make between a narrow and a broad sense of ‘meaning of the words’; if so, I meant it in the broad sense.
By the way, what do you think about the rigid designator variant in the case of red and blue?

Do they disagree that there are cars and doors, or just that cars have doors?
The person I have in mind would deny that there are cars (since if there were cars, they would have doors).
He would deny options b and c and argue against commonsense claims about cars using a sorites style argument (whether justifiedly or not).
I find the rigid designator case hard to asses without a definition of the term ‘x rigidly designates y’. (Rocks at the bottom again!)

Thanks, Joshua,
And I agree we’re hitting rock bottom, but I think there is still some room for some brief drilling.
1.

The person I have in mind would deny that there are cars (since if there were cars, they would have doors).
He would deny options b and c and argue against commonsense claims about cars using a sorites style argument (whether justifiedly or not).

I’m not sure I’m tracking. Option c. is the ‘other’ option, so if it’s neither a. nor b., it’s c. But he wouldn’t accept a., from what I read, so I’m not sure why he would deny b. and c. Maybe he would deny a. and b.? (if that was a typo?) Please, clarify.
In any case, that answer does give me a lot of information.
For instance, his position would be that if, say, the media reports that many people died in a massive crash involving many cars, the media reports are false, and that if someone says that electric cars are less common than combustion cars, that’s not true, either, etc.
As you may imagine, I disagree with that view, but I still get the impression that the problem is meaning.
You say that it’s a sorites style argument.
While I don’t know what argument you’re thinking about (a brief sketch might help), that makes me think of something similar to the case of elephants earlier. So, let’s start with the image of a car. Let’s gradually change it until we get a truck, on screen. At which point does the transition from ‘car’ to ‘not a car’ takes place?
Of course, at least as a thought experiment, we can do the same with actual stuff, rather than images. Let’s start with a car, make a very similar one, etc.
Is that the kind of argument he has in mind?
If so, I would disagree with the view that the word ‘car’ (and generally, the words we use to describe the world around us) entail an ontological commitment to that arbitrary degree of precision.
But what seems to be clear is that there is no commitment to that level of precision. I would simply say that (as in the case of elephants) there is no objective fact of the matter as to whether some objects are (or some images represent) cars.
Maybe something similar to prototype theory is correct. Maybe there are necessary and sufficient conditions as long as they too may be fuzzy, or variable between observers and for an observer at different time; there are a few options, but the sorites based approach (if my hypothesis of what kind of sorites-style argument is correct) is wrong.
Nevertheless, that disagreement seems to be about the ontological commitments one entails by making statements implying the existence of cars, which seems to be a matter of language, and in particular about the meaning of ‘car’ (or, for that matter, ‘elephant’, and other words)…though I guess perhaps you’re not using ‘meaning’ in the same sense I’m using it, and that explains the difference? (which would mean our apparent disagreement would be the result of a semantic difference too)
By the way, and out of curiosity, would he deny the existence of elephants as well, or does he make a distinction for some kind of biological organisms, minds, etc.? (if he does that, I would be intrigued by how he would react to a sorites styles argument against the existence of elephants).
On the other hand, if what I described above is not the kind of sorites style argument that you have in mind, then I’d like to ask for a (very brief) sketch, if you don’t mind, so I can try to assess where the disagreement lies (I find this case more and more intriguing).
4. I’ve been thinking about that, and realized that definitions of ‘rigid designator’ usually are given in terms of other terms which in turn might be interpreted differently by you and me.
So, I thought that the ‘rigid designator’ case might be useful as a means of assessing whether our concepts of respective understandings of the term ‘rigid designator’ are similar enough, or not (i.e., if you don’t think it’s a rigid designator and you let me know why, maybe we can discuss it and reach an agreement as to whether it’s a rigid designator, or maybe lack of agreement will suggest differences in the usage of ‘rigid designator’).
Other than that, we can I suppose try some definitions, or maybe better some examples, to see if we at least agree on the paradigmatic cases.
At any rate, there may be an alternative to including the term ‘rigid designator’ in my proposal about metaphysical impossibility. Instead of using that term, I may try to point at some examples, so that you would grasp what it is that I mean. Still, there is a difficulty in that unless perhaps I list like a zillion examples (and perhaps even then), it may well be that you’re going to grasp some pattern my examples have in common but which is different from the pattern I picked…but it’s an option still available (only plausibly not with the zillion examples), at least if nothing else works.

Angra,
1. I meant a and b (my bad). Here’s a nice discussion of the type of argument (except supposing that nihilism is more plausible than universalism): http://faculty.las.illinois.edu/dzkorman/Vagueness.pdf
4. I’m tracking you. I’m curious what you make of this claim: ‘it is impossible that abstract entities ontologically exist’. Do you think it’s true? If so, do you take it that ‘abstract entities ontologically exist’ strictly entails a contradiction (or that its impossibility is discerned via the rigid designation / meaning of terms)?

Joshua,
1. Thanks for the link. Some of my thoughts on (parts of) the arguments in that paper (other issues would need perhaps more time) would be:
a. The universalist answer depends on a broad conception of ‘object’. I do not know whether that’s the colloquial meaning, though as I mentioned, it may very well be that there is more than one colloquial meaning, and one of those meanings is very broad (and in that sense, universalism is true), whereas one or more other senses of ‘object’ are such that universalism is false. In fact, I think this situation is quite plausible.
However, even though I find it plausible that there is one common sense of ‘object’ or ‘composed object’ under which universalism is false, I also believe that that word too is vague, so I would not accept (A1).
b. In the argument in question, we may leave aside the issue of whether there are composed objects, and address the specific issue of whether (or when) there is a hammer, as the hammer is being made. At the beginning of the process, there is no hammer (not in that place, anyway). At the end of it, there is one. When is the first moment at which there is one? If one goes slowly enough, I think there is no objective fact of the matter. But I see that as very probably similar from the case of, say, elephants, dogs, humans, even persons, and so on. I definitely would reject the idea that there is nothing of the sort.
c. I also reject the idea that there can’t be count indeterminacy. Just as I don’t see why there couldn’t be can be indeterminacy about, say, how many lions there are, or how many elephants, or how many cars, etc., I don’t see why there couldn’t be indeterminacy about how many concrete objects there are.
The problem is the indeterminacy of the word ‘object’, at least in some of its usages.
But all of this looks to me like a matter of language, not ontology. Let’s say that the handle and the head of the hammer are being slowly fused. At which point is there for the first time one concrete object ‘hammer’, rather than two (‘head’ and ‘handle’)?
As I mentioned, if it’s slowly enough, I would say that there is no objective fact of the matter, but that’s a question of how the words ‘object’ (in some limited sense) are used, not about (in a non-philosophical but I hope clear enough expression) what stuff is out there: we see the head and the handle getting closer, being put together, etc., and we (well, most of us) trust our senses that all that stuff is indeed in front of our eyes. What dispute is there, other than about whether some words have some meaning such that they refer to the stuff in question? (granted, differences about the meaning of words in many cases do result in other kinds of disagreements, but at this point I’m not seeing it).
As for the claim that numerical sentences do not contain any vague expressions, that may be true (still somewhat debatable, but let’s leave that aside) as long as we’re talking about entirely numerical sentences. On the other hand, if there are vague expressions (and I think there very probably are), then surely the same goes for partially numerical sentences: one just needs to combine numerical claims with some vague expressions in a suitable manner.
So, I don’t think that the argument based on numerical indeterminacy ought to be accepted unless one already accepts no vague expressions.
d. I disagree with the claim that universalism has an ontology of strange fusions, if that strangeness is meant to be a claim about reality beyond our language. If one simply defines ‘object’ in a very broad manner (which may well be one of the common usages, even if not the most frequent one), clearly there are such ‘fusions’, but there is nothing strange about them, since that they exist follows clearly from the definition of the words, and that’s a matter of classifying the world around us, not about how the world around us is.
I do think that universalism is false under some conceptions of ‘object’ (perhaps, the most frequently used), but then again, that’s unproblematic from my perspective. The puzzles seem to be about human language and human psychology â difficult matters no doubt, but it’s not the kind of difficulty that seems to be suggested in the paper, imho.
e. I’m not sure I’m being clear enough about some of these issues. Perhaps, more elaboration of the meaning of ‘vague’, etc., would be required.
f. All that said, I’m still curious about the idea of running a sorites style argument against the existence of elephants and test whether (some) philosophers who reject the existence of cars would also reject that of elephants (and if so, I have other sorites-like ideas in mind). Do you know whether your friend would reject the existence of elephants due to sorites style arguments? Or do you think that maybe he’ll make some kind of mind-based distinction, or some other reply?
4. It’s an interesting yet complicated matter. To simplify it a little, let’s consider natural prime numbers (I would apply the same considerations to other abstracta; I’m leaving aside perhaps some claims the game of chess and the like, in which I think the meaning of the words is different but in the end the ontologically committed ordinary talk is talk about concreta).
Given that I don’t believe that in ordinary math talk ‘there are infinitely many prime numbers’ is an ontological claim, a question here is: what would it mean to say that, in the ontological sense, there are infinitely many prime numbers?
A possibility is that such a claim is (or at least entails) that ordinary math talk is such that ‘there are infinitely many prime numbers’ is indeed and ontological claim, and also a true one.
If so, then that claim contains or entails, in my view, a false claim about what the meaning of ordinary language actually is, more precisely about the actual meaning of ordinary math talk in that case. But such a claim is surely fixed by what happens at the actual world, so I would say it’s impossible.
But perhaps, someone might make a different ontological claim, stating that there are infinitely many prime numbers in the ontological sense, but without saying or implying that in the usual sense ‘there are infinitely many prime numbers’ is an ontological claim.
That would be very unusual, it seems to me. As far as I know, philosophers who make ontological claims about prime numbers usually maintain that the claims in question are the usual claims about them. So, I would have to ask what the person making such an unusual claim means by it, since they’re not using the words in the usual sense at all (e.g., what’s an ontological prime number?)
On the other hand, if I’m wrong and the usual claim is an ontological claim, then I’m not sure I grasp it. It seems to me that I am not making such a claim, so if the usual claim is an ontological claim, it seems to me that I’ve just come up (oddly) with a parallel that allows me to do math just fine, for some reason. It would be odd, and I still would need to know what the usual claim means before I make a more detailed analysis…
And what if I’m wrong about that too, and even my usual talk about prime numbers is an ontological claim?
In that case, I think I would be too mistaken about the matter to make any proper assessment, so in that case, I don’t know whether the claim is impossible. My reaction under that assumption would probably be to keep doing math as before, without taking a stance on other issues until I have more information.

Angra,
1. Just to be sure, the nihilist I have in mind is working with the broad notion of ‘object’ and simply disagrees with the universalist even given that notion. You seem to take it as obvious that on the broad notion, universalism is true (just by definition), but the nihilist will say that your intuitions mislead you. In other words, he doesn’t disagree with your definition. He disagrees about the nature of the stuff out there — over how many objects (in the broadest sense) there are.
f. My friend makes a mind-based distinction, according to which persons (and other mental substances) are simples (and they don’t have bodies, because bodies don’t exist).
4. I don’t recognize any distinction between an ontologically committing meaning of ‘there is’ and the ordinary meaning that mathematicians work with. Hence, I agree with Mark Balaguer that the nominalist should be a fictionalist: they should deny that mathematical statements are true; ‘2+2=4’ is true in the fictional (false) story of math, but it is false simpliciter.
But these are deeply controversial matters. Your answer makes sense; thanks.

Let me try this:
Either the Peano axioms are implicit definitions of the term ‘natural number’ or they are ontological claims. In the latter case, their necessity isn’t derivable by the meanings of the terms. So, suppose the former. Then consider the statement N: ‘there is (in whatever ordinary sense of “there is” you understand) an x, such that x is a natural number’, where ‘natural number’ is implicitly defined by the Peano axioms. N is either necessarily true or necessarily false (it seems to me). Do you think N’s necessity or impossibility is deducible by your criteria?

Joshua,
1. Let me try to clarify some of my views:
g. When I said that the universalist assumes the broad conception of ‘object’, I meant it was a necessary condition in the universalist argument in question, not a sufficient one for universalism about composition. Sorry if that wasn’t clear.
h. That said, I do think that by that broad conception of ‘object’, pretty much anything compose an object. But the nihilist you have in mind would disagree. That seems to be a disagreement about the meaning of ‘part’, and/or ‘compose’…or maybe ‘object’.
On that note, I’m not entirely sure on what point he would be saying that my intuitions mislead me. Is it about the existence of objects, in that broadest sense, or of parts?
In any case:
i. On the broadest notion of “object”, I say there are objects like cars, hammers, etc.If he disagrees with that, then the disagreement appears to be about the meaning of ‘object’ in the broadest sense. In other words, stipulating that the sense of ‘object’ is the broadest one does not guarantee that we actually have a shared understanding of it. We may have different understandings of ‘object’, and the broadest sense each of us comes up with is different.
On the other hand, if he agrees that on that notion of object, there are cars, hammers, etc., which are objects (but it seems not; you said he believes there are no cars), then:
j. The doors are parts of normal cars, which are objects. He disagrees with that, but then, if there is a disagreement there, it seems, about what conditions an object (like a door) needs to meet in order to be a part of another one (like a car), and so we’re back to a disagreement on the meaning of ‘parts’.
k. In any event, when it comes to what your nihilist friend holds, we may leave the notion of ‘object’ aside, as I mentioned earlier. I addressed ‘object’ in my immediately previous reply because I was addressing the paper you linked to. If we go back to the issue of what your friend holds, then we may just consider whether or not cars, hammers or elephants exist, and if they do, whether they have parts. One way or another, he disagrees on one of the points, and the result seems to be either on the meaning of ‘car’, ‘hammer’, ‘elephant’, etc., or the meaning of ‘parts’, or more than one of those.If you’re not sure that that’s what the disagreement is about, or find it implausible, etc. (I’m not entirely sure what your take on this is), I would ask what else you suspect that the disagreement is about, or alternatively what you think what he would think that the disagreement is about?
l. I hope we won’t run out of letters. 😉
f.

f. My friend makes a mind-based distinction, according to which persons (and other mental substances) are simples (and they don’t have bodies, because bodies don’t exist).

Great, so let me sketch sorites like argument for elephants as an introduction:
Let’s start at some time t0 about 1 billion years ago; the exact moment is not important, as long as it’s fixed. There were no elephants (If he thinks there were elephants at that time, let’s go back 12 billion years. If he still believes there were elephants, then let’s go back as long as needed so that there were no elephants. If he believes that elephants have always existed perhaps because of some belief that all minds always existed, please let me know and I’ll adjust my arguments accordingly).
Let’s move forward in time one Planck Time E at a time.
If he rejects the sorites like argument (and he ought to if he holds that there are elephants), then he would have to accept that there is some minimum n1, such that at t1= t0+n1*E, there is at least one elephant, and yet at t1-E there were no elephants.
Given that different people very probably have slightly different concepts of ‘elephant’, I find that improbable (moreover, even for a single person, it’s not clear whether their concept is precise enough at a given time. Maybe in some borderline cases, and depending on how an entity is introduced to them, they would or would not be disposed to call it ‘elephant’, and no irrationality can be found; but maybe not; in any case, this is not crucial to my argument).
But let’s say that he’s right and there is such first t1.
In that case, why would he accept the sorites like argument in other circumstances and cases, like a car, a truck or a hammer?
From a different perspective, why would he believe (if he does) that words like ‘elephant’ have such degree of accuracy, but words like ‘car’, or ‘hammer’ do not?
Sorites style arguments do not seem to provide any evidence of that. They do not say anything about whether some particular words are more precise than others, at least as far as I can tell.
On the other hand, if it’s not the case that he believes that there is any particular difference in accuracy of the words and consider them all to be accurate to any arbitrary degree (I disagree with that, so that’s a difference about meaning, but let’s leave that disagreement aside for a moment), then how does a sorites style argument would work?
After all, if there is such accuracy, then wherever the cut off line is, there is always a cut off line. Why not for cars, or hammers?
4. Thanks for that explanation. I do agree that they’re controversial matters (by the way, I think we might have a different take on fiction as well).
Regarding the fictionalist account, there might be some differences if someone is playing a role, and that complicates matters, but I think the analogy is reasonably good if we leave that particular kind of situation aside. Maybe a closer analogy (not perfect; it’s an analogy, but close enough to explain my view I hope) would be a hypothetical scenario like many of the ones usually used in philosophy; let’s say one of the non-contradictory scenarios.
For example, we may consider certain scenario, in which some people behave in such-and-such way, and make assessments about, say, whether those people are acting rationally, etc. We may even make existential claims in that context. Are those assessments true?
I think generally yes (unless one makes a mistake in some specific case, but that’s another matter).
For a more detailed example, we may consider the thread about infinite multiverse and probability.
In the context of assessing some things in the scenario presented in the OP, I might say ‘There are infinitely many Joneses and an angel talking to them’, etc.
Would I be making a false claim, or a true one?
I would say a true one.
It wouldn’t be true if my claim were that there are such people ‘out there’, so to speak. But it’s not. The domain is the scenario in question (which identified by pointing to the thread in question), so in that context, my assertion ‘There are infinitely many Joneses and an angel talking to them’ would be, as I understand these matters, true.
So, let’s consider a mathematical case:
PR: There are infinitely many prime natural numbers.
Is PR true?
If it’s a claim that they exist somehow ‘out there’, then no.
But if my domain is the set of natural numbers, or some category ‘natural numbers’ of all objects (even hypothetical) that meet certain conditions, then it seems to me PR is true.
In order for the fictionalist to conclude that PR is false in the usual sense of the words (if he concludes that), I get the impression that he’s implicitly holding that PR is by default, in the usual sense of the words a claim about the world around us.
I would reject that assumption.
If I’m mistaken, it seems to me that my mistake is about the meaning of the meaning of the sentence PR in the usual sense, or about the meaning of ‘true’, or some other meaning.

Either the Peano axioms are implicit definitions of the term ‘natural number’ or they are ontological claims.Â

I’m not sure I would agree with that.
It may be that the term ‘natural number’ alone does not contain those implicit definitions, but ‘set of natural numbers’, or more precisely the category/scenario (which turns out to be a set) of all (hypothetical) objects that meet the criteria for being a natural number (identified up to an isomorphism), does.
That category may be intuitively apprehended in many ways, but for instance:
– We observe 1 object (say, an apple), the another one, etc., then two objects, and eventually we intuitively group groups of objects by their cardinality, and from that we get the concepts of 1, 2, 3, and a few others.
– From there, we also get (by examples, if needed) the concept of successor, sum, etc.
– Then, the category would be something like: {1, 2, 3, 4, .., all of those; the relations are the usually apprehended ones}
It’s not entirely clear to me (it’s a complicated matter) whether it’s equivalent to look at it from the perspective of meaning of the terms describing the individual objects only (numbers, in this case) and then consider the category of all hypothetical objects that meet the criteria, or from the perspective of the meaning of the terms describing a certain intuitive scenario or category which contains some objects (like ‘natural numbers’, or ‘all hereditary sets’).
In any event, when I talk about numbers, I do seem to have the category ‘natural numbers’ as my domain of talk (as I might have the domain ‘scenario in the OP in the thread about the multiverse and probability’, and I might assert ‘there are infinitely many Joneses and an angel’, though the analogy is not so good here because in that case one might consider what’s possible from the perspective of the characters of the scenario, which changes things completely).
Side note: the psychological account above is an example; in many cases in mathematics, we learn by starting with the axioms, and then we talk about all objects that meet certain conditions, etc.; there are options, but the example seems to give a potential account of how people came up with that particular category, in the case of natural numbers.

So, suppose the former. Then consider the statement N: ‘there is (in whatever ordinary sense of “there is” you understand) an x, such that x is a natural number’, where ‘natural number’ is implicitly defined by the Peano axioms. N is either necessarily true or necessarily false (it seems to me). Do you think N’s necessity or impossibility is deducible by your criteria?

As I understand it, its necessity is.
The category would be here all (hypothetical) objects that meet certain conditions (i.e., ‘natural numbers’) identified up to isomorphism by those conditions. The category (which turns out to be a set) is clearly non-empty, whether we start with 1, 2, 3, and we say ‘it’s the category containing all of those and nothing else’, or just the category of all objects (hypothetical if needed) that meet the criteria, etc.
A perhaps interesting issue arises if (for instance), we consider the category of all hereditary sets and propose, say, the axiom of regularity. At that point, different people might have different intuitive concepts. But the solution is that some statements are necessary in some of the categories (i.e., defined by some people), and not in the categories defined by others; this is not a problem in practice, since we may agree (one way or another) on a given set of axioms, and then people define the categories based on them (rather than the other way around; most people don’t get to choose axioms for the (a) mathematics community, but rather learn with the given axioms).

Thanks for all that, Angra.
1. In other words, stipulating that the sense of ‘object’ is the broadest one does not guarantee that we actually have a shared understanding of it. Nice point. I agree there is no absolute guarantee. I’m just saying that I haven’t been able to discern a difference in what he and I mean by the terms, and I doubt there is a difference. It seems more plausible to me that we have the same basic meanings in mind, and the disagreement is over the truth of the proposition expressed; yet I agree that you can tell a story about why appearances are misleading, etc. (Sorry to be brief, and I hope it’s okay, but I’m not going to attempt to represent his reasons more precisely, because I’m not in a position to do so. But you raise interesting questions; thanks.)
4. Do you think, then, that “there are some (hypothetical) objects, such as sets” is strictly necessary? Also, if you wish, might you define ‘x is an ontological claim’? I’m not sure what you mean by that.

Nice point. I agree there is no absolute guarantee. I’m just saying that I haven’t been able to discern a difference in what he and I mean by the terms, and I doubt there is a difference. It seems more plausible to me that we have the same basic meanings in mind, and the disagreement is over the truth of the proposition expressed; yet I agree that you can tell a story about why appearances are misleading, etc.

I was trying to be thorough, but your observation is good evidence that our respective usage of ‘object’ in the broadest sense is very similar.
Also, upon further consideration, it seems to me that our disagreement is very likely not to the result of a difference in which we intuitively understand the word ‘object’, because regardless of whether there is such a difference in the case of ‘object’, in other cases it’s almost certain that he and I use the words in almost the same sense, and the disagreement persists.
For example, cases like that would be terms like ‘car’, ‘hammer’, ‘cell phone’, ‘bicycle’, etc. We’ve all learned those terms in a very similar manner, and we’re all similar enough.
So, while I do think that there are minuscule differences in the way he grasps and uses those and many other words and the way I do (because I think that’s generally the case among humans), and which would probably show up if one were able to actually set up the…sorites-like slow transformation? – or whatever it’s called -, I don’t think that that is the root of our disagreement. For example, those minuscule differences would not explain a disagreement about, say, whether I have a cell phone.
On the other hand, I still get the impression that we have a disagreement about the meaning of some terms, in the sense that he has a theory (implicit of otherwise) about what some of those terms mean (or at least, about part of the meaning of the terms, including certain ontological commitments) and which I reject.
I’m not sure I’m being clear here.
Perhaps, the following analogy will clarify what I’m getting at (and I’m not saying that your friend’s hypothesis is nearly as unsophisticated; it’s just to try to clarify my view):
Let’s say that Bob has the theory that ‘Behavior X is immoral’ means ‘God forbids behavior X’, whereas Alice believes that that’s not what ‘Behavior X is immoral’ means.
Then, Bob and Alice disagree about the meaning of some moral terms. But that does not mean that Bob and Alice actually have a considerably different grasp of moral terms, and that when they say ‘Behavior X is immoral’, they mean very different things.
In fact, in normal cases at least, that would not be true (if it were true, that could be used in a case against moral realism, but I’m not suggesting it’s true). The disagreement would be in their theories about what some words mean, but even then, they would not be using the words differently, at least most of the time.
That’s what I’m trying to get at here. After considering the matter for a while, and at least given the information I have at this point, it seems plausible to me that the disagreement between your friend and me about whether, say, I have a cell phone, is very probably not a difference in the way we normally understand ‘cell phone’, or ‘have’, or ‘I’, but rather, a difference in a theory about the meaning of the words (which he may hold explicitly or implicitly).

(Sorry to be brief, and I hope it’s okay, but I’m not going to attempt to represent his reasons more precisely, because I’m not in a position to do so. But you raise interesting questions; thanks.)

No problems; thanks for your interesting points as well.
And sorry to be not-brief. I’m trying to be clear, and some of the issues are difficult for me.
4.

Â Do you think, then, that “there are some (hypothetical) objects, such as sets” is strictly necessary?Â

I’ll get to that in a moment, but first I’d like to say that I used ‘hypothetical’ as a way of designating the category and explaining where the quantifiers ranged over, but after further consideration, I’m thinking ‘hypothetical’ might not be entirely clear (e.g., in a hypothetical scenario like S1, are there infinitely many Joneses, or infinitely many hypothetical Joneses? They’re not hypothetical as part of the scenario, but they are in the sense the scenario is so; I hope the difference is clear).
So, I think it’s preferable to define the hypothetical scenario by demonstration (e.g., ‘natural numbers’ contains {1, 2, 3..}, and all of those and no more).
That is similar in a way to defining a scenario (say, S2), saying that in that scenario, there are three people, namely Angel the angel, Jones and Smith who are humans, and Jones rolls a die [potentially] infinitely many times, etc. (I described some scenarios like that in greater detail in the thread about the multiverse and probability), and then make assessment about that scenario.
There are some differences between S2 and math, though. For instance, in the case of S2, one may look at claims of necessity from within or outside the scenario.
P1: In S2, Smith exists. [one may leave aside the S2, if it’s implicit in context]
P2: In S2, necessarily Smith exists.
If P1 is understood as a claim about the what obtains in the scenario as described (i.e., S2 fixes the referent), then P1 is true, and even necessarily true (the referent is already fixed, and so by the description of the scenario S2 (not a modification of it), we get necessity).
On the other hand, P2 is false, because in that case one is assessing the matter from within the scenario (rather than describing the scenario, and then claiming necessity of the description with the fixed referent), and in that scenario, it’s not true that Smith exists necessarily.
I don’t know that there is a similar issue (like P2) in the case of, say, the natural numbers.
All that aside, I guess you may ask whether I think that “there are (hypothetical) objects” or “there are hypothetical objects” simpliciter is necessarily true.
In that case, I would understand the term ‘simpliciter’ to reflect some ordinary usage (i.e., no additional claims), but I don’t know of an ordinary usage of an expression like that.
So, I’ll consider options:
I: If “There are objects’ is like ‘There are planets’ (crudely, ‘out there’), then my answer would be no, I don’t think it’s necessarily true that there are objects.
As for hypothetical objects, it’s somewhat ambiguous.
II: If ‘there are hypothetical objects’ is some claim about a Platonic realm or some mind-independent stuff, I wouldn’t accept it.
III: Leaving the ambiguity I mentioned in the Joneses’ case aside, if we count numbers as hypothetical objects (even though they’re hypothetical from outside the scenario so to speak), then since I think that there are infinitely many primes is necessarily true in the usual sense, I would also say (in a similar sense) that there are hypothetical objects is so…but still, I think the ‘hypothetical’ part is not clear. Sorry I introduced it (I thought it would make my view more clear, but I realize it didn’t).

Also, if you wish, might you define ‘x is an ontological claim’? I’m not sure what you mean by that.

I would define it if I knew how to, but I don’t, other than by saying it’s a claim about the existence of some entity (in a strict sense, which I think is the one you’re asking about), or (in a broader sense), that commits the claimant to the existence of some entity (because of what the claim entails), but that only leads us to the issue of the meaning of ‘entity’…and that’s a problem.
I considered the use of ‘mind-independent’, but that term is (in my view) very ambiguous as well, and probably does not reflect what I mean, either, since claims about the existence of minds would count.
Maybe the rather crude and non-philosophical ‘out there’ would work better..but what if it’s ‘in here’ (e,g., claims about minds), and also, it might not be clear enough.
An alternative would be to try by means of examples of what I take to be ontological claims, and what I don’t, but I’m not sure it will work, and I might have to use some of the concepts above.
But still, examples of ontological claims as I understand the words (usual sense of the words, including usual contexts) would be:
o1. There are planets orbiting the Sun.
o2. There are infinitely many galaxies.
o3. There are chimpanzees.
o4. There are cars, and trucks, and cell phones.
o5. Our universe was created by an omnipotent, omniscient, morally perfect being who also created all other beings. [not strictly a claim of existence, but it entails it, so let’s say it’s ontologically committed, or an ontological claim in a broad sense].
Some claims I take not to be ontological claims (but still true, in usual contexts, or in the ones I’ll specify):
no1: There are Jedi Knights. [implicit: the claim is about the ‘star wars’ story. Usually, the person asserting that is not committed to the existence of them, but describing the story; there may be an implicit assumption that someone wrote the story and others know it, but the claim itself is not about that, it seems to me. On the other hand, if a character were to make that claim, it would be an ontological claim on the part of the character].
no2: In S1 [the scenario in the other thread] there are infinitely many Joneses. [but this would be an ontological claim if there is a commitment to a Platonic realm of scenarios, or stories, etc.]-
no3: There are infinitely many prime numbers. [if my take on this is correct, or something like it; if, on the other hand, that’s a claim about some Platonic Realm, then that would seem to be an ontological claim, though I have some difficulty grasping Platonic claims].
no4: Darth Vader was an evil person. [not committed to the existence of Darth Vader].
Perhaps, the following example is better (or not):
Let’s say that Bob defends an Anselm-like simple ontological argument. Alice rejects the argument, and so the exchange goes (for instance; it’s an example, not a counterargument against simple OA):
Bob: Let’s define ‘God’ as a being such that no greater being can be conceived of.
If God did not exist, we could conceive of a greater one â namely, one as powerful, good, knowledgeable, etc., but who exists.
Alice: There is a difference between whether among all conceivable beings, there is one that is maximal with respect to greatness, and whether such an entity actually exists.
For instance, in the category ‘all conceivable maximally evil beings’, there is one that is maximal with respect to greatness â namely, a maximally powerful, maximally knowledgeable one.
But that does not mean that the being in question exists. I deny that he does.
In that case, when Alice said that there is a being in that category that is maximal with respect to greatness (also, I’m not claiming there is), she did not make an ontological claim.
On the other hand, when Bob said that there is a maximally great being, he did.
Crudely put, Bob’s maximally great being is ‘out there’, whereas Alice’s maximally evil being who is maximal with respect to greatness is not ‘out there’, but she’s talking about a subcategory of the category ‘conceivable beings’ (arguably, perhaps the category should be called ‘conceivable partially defined beings’, since the characteristics (at least, in the case of the non-existent ones) are not fully determined; but that’s another topic I think).
I’m afraid that’s all I’ve managed to come up with so far; I’ll try to think of a definition, or better examples.

That’s all very interesting and helpful. Thanks, Angra. I think we’ve brought out a lot of relevant issues. We could probably continue to do more, but I’m content to leave it here.
Our exchange nicely displays the relevance of one’s understanding of modal notions to assessing GR-type arguments. That’s my concluding remark. (Any final remarks go to you, if you wish to add anything further.)

Joshua,
Thanks to you as well, and I agree with your concluding remark. I don’t have further remarks on the matter, but thank you for the consideration.
Side note: before I read your post above, I’d written a brief but somewhat more detailed and I think clearer explanation of why I still think that your (parts/cars/some other objects)-nihilist friend and I probably disagree on some issue regarding the meaning of terms; please let me know if you’re interested and I’ll post it or mail it).

I don’t think it an overstatement to say that the concept of the infinite plays a key role in the philosophy of religion. There are at least two senses in which ‘infinite’ is used. First, ‘infinite’ is often used to mean maximal, as in God’s infinite …